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Journal articles on the topic 'Almost complex manifold'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 March 2023

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1

KIM, JIN HONG. "EXAMPLES OF COMPACT NEGATIVELY CURVED ALMOST COMPLEX, BUT NOT COMPLEX, MANIFOLDS." International Journal of Geometric Methods in Modern Physics 09, no. 07 (September 7, 2012): 1220012. http://dx.doi.org/10.1142/s0219887812200125.

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In this paper, we provide infinitely many examples of compact negatively curved almost complex, but not complex, manifolds of complex dimension 2n + 1 or 2n + 2 by using strongly pseudoconvex homogeneous domains in an almost complex manifold. Unlike the Kodaira–Thurston manifold which is the flat case, the first Betti number of the constructed manifolds is even, and their first homology group is, in fact, isomorphic to ℤ4n+2 or ℤ4n+4.

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2

ANGELLA, DANIELE, and ADRIANO TOMASSINI. "ON THE COHOMOLOGY OF ALMOST-COMPLEX MANIFOLDS." International Journal of Mathematics 23, no. 02 (February 2012): 1250019. http://dx.doi.org/10.1142/s0129167x11007604.

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Following [T.-J. Li and W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.17(4) (2009) 651–683], we continue to study the link between the cohomology of an almost-complex manifold and its almost-complex structure. In particular, we apply the same argument in [T.-J. Li and W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.17(4) (2009) 651–683] and the results obtained by [D. Sullivan, Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math.36(1) (1976) 225–255] to study the cone of semi-Kähler structures on a compact semi-Kähler manifold.

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3

Manev, Mancho. "On canonical-type connections on almost contact complex Riemannian manifolds." Filomat 29, no. 3 (2015): 411–25. http://dx.doi.org/10.2298/fil1503411m.

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We consider a pair of smooth manifolds, which are the counterparts in the even-dimensional and odd-dimensional cases. They are separately an almost complex manifold with Norden metric and an almost contact manifolds with B-metric, respectively. They can be combined as the so-called almost contact complex Riemannian manifold. This paper is a survey with additions of results on differential geometry of canonical-type connections (i.e. metric connections with torsion satisfying a certain algebraic identity) on the considered manifolds.

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4

Kumar, Rakesh, Garima Gupta, and Rachna Rani. "Adapted connections on Kaehler–Norden Golden manifolds and harmonicity." International Journal of Geometric Methods in Modern Physics 17, no. 02 (February 2020): 2050027. http://dx.doi.org/10.1142/s0219887820500279.

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We study almost complex Norden Golden manifolds and Kaehler–Norden Golden manifolds. We derive connections adapted to almost complex Norden Golden structure of an almost complex Norden Golden manifold and of a Kaehler–Norden Golden manifold. We also set up a necessary and sufficient condition for the integrability of almost complex Norden Golden structure. We define twin Norden Golden Hessian metric for a Kaehler–Norden Golden Hessian manifold. Finally, we prove that a complex Norden Golden map between Kaehler–Norden Golden manifolds is a harmonic map.

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5

Cirici, Joana, and Scott O. Wilson. "Almost Hermitian Identities." Mathematics 8, no. 8 (August 13, 2020): 1357. http://dx.doi.org/10.3390/math8081357.

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We study the local commutation relation between the Lefschetz operator and the exterior differential on an almost complex manifold with a compatible metric. The identity that we obtain generalizes the backbone of the local Kähler identities to the setting of almost Hermitian manifolds, allowing for new global results for such manifolds.

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6

KUMAR, PRADIP. "ALMOST COMPLEX STRUCTURE ON PATH SPACE." International Journal of Geometric Methods in Modern Physics 10, no. 03 (January 10, 2013): 1220034. http://dx.doi.org/10.1142/s0219887812200344.

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Let M be a complex manifold and let PM ≔ C∞([0, 1], M) be space of smooth paths over M. We prove that the induced almost complex structure on PM is weak integrable by extending the result of Indranil Biswas and Saikat Chatterjee of [Geometric structures on path spaces, Int. J. Geom. Meth. Mod. Phys.8(7) (2011) 1553–1569]. Further we prove that if M is smooth manifold with corner and N is any complex manifold then induced almost complex structure 𝔍 on Fréchet manifold C∞(M, N) is weak integrable.

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7

Bejan, Cornelia-Livia, and Galia Nakova. "Almost Complex and Hypercomplex Norden Structures Induced by Natural Riemann Extensions." Mathematics 10, no. 15 (July 27, 2022): 2625. http://dx.doi.org/10.3390/math10152625.

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The Riemann extension, introduced by E. K. Patterson and A. G. Walker, is a semi-Riemannian metric with a neutral signature on the cotangent bundle T∗M of a smooth manifold M, induced by a symmetric linear connection ∇ on M. In this paper we deal with a natural Riemann extension g¯, which is a generalization (due to M. Sekizawa and O. Kowalski) of the Riemann extension. We construct an almost complex structure J¯ on the cotangent bundle T∗M of an almost complex manifold (M,J,∇) with a symmetric linear connection ∇ such that (T∗M,J¯,g¯) is an almost complex manifold, where the natural Riemann extension g¯ is a Norden metric. We obtain necessary and sufficient conditions for (T∗M,J¯,g¯) to belong to the main classes of the Ganchev–Borisov classification of the almost complex manifolds with Norden metric. We also examine the cases when the base manifold is an almost complex manifold with Norden metric or it is a complex manifold (M,J,∇′) endowed with an almost complex connection ∇′ (∇′J=0). We investigate the harmonicity with respect to g¯ of the almost complex structure J¯, according to the type of the base manifold. Moreover, we define an almost hypercomplex structure (J¯1,J¯2,J¯3) on the cotangent bundle T∗M4n of an almost hypercomplex manifold (M4n,J1,J2,J3,∇) with a symmetric linear connection ∇. The natural Riemann extension g¯ is a Hermitian metric with respect to J¯1 and a Norden metric with respect to J¯2 and J¯3.

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8

Merker, Jochen. "On Almost Hyper-Para-Kähler Manifolds." ISRN Geometry 2012 (March 8, 2012): 1–13. http://dx.doi.org/10.5402/2012/535101.

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In this paper it is shown that a -dimensional almost symplectic manifold can be endowed with an almost paracomplex structure , , and an almost complex structure , , satisfying for , for and , if and only if the structure group of can be reduced from (or ) to . In the symplectic case such a manifold is called an almost hyper-para-Kähler manifold. Topological and metric properties of almost hyper-para-Kähler manifolds as well as integrability of are discussed. It is especially shown that the Pontrjagin classes of the eigenbundles of to the eigenvalues depend only on the symplectic structure and not on the choice of .

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9

Sukhov, Alexandre Borisovich. "Discs and boundary uniqueness for psh functions on almost complex manifold." Ufimskii Matematicheskii Zhurnal 10, no. 4 (2018): 129–36. http://dx.doi.org/10.13108/2018-10-4-129.

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10

Manev, Mancho. "Almost Riemann Solitons with Vertical Potential on Conformal Cosymplectic Contact Complex Riemannian Manifolds." Symmetry 15, no. 1 (December 30, 2022): 104. http://dx.doi.org/10.3390/sym15010104.

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Almost-Riemann solitons are introduced and studied on an almost contact complex Riemannian manifold, i.e., an almost-contact B-metric manifold, which is obtained from a cosymplectic manifold of the considered type by means of a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The potential of the studied soliton is assumed to be in the vertical distribution, i.e., it is collinear to the Reeb vector field. In this way, manifolds from the four main classes of the studied manifolds are obtained. The curvature properties of the resulting manifolds are derived. An explicit example of dimension five is constructed. The Bochner curvature tensor is used (for a dimension of at least seven) as a conformal invariant to obtain these properties and to construct an explicit example in relation to the obtained results.

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11

MA, LI. "Moduli space of special Lagrangians in almost Kahler spaces." Anais da Academia Brasileira de Ciências 73, no. 1 (March 2001): 01–05. http://dx.doi.org/10.1590/s0001-37652001000100001.

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12

Kawamura, Masaya. "On Kähler-like and G-Kähler-like almost Hermitian manifolds." Complex Manifolds 7, no. 1 (April 3, 2020): 145–61. http://dx.doi.org/10.1515/coma-2020-0009.

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AbstractWe introduce Kähler-like, G-Kähler-like metrics on almost Hermitian manifolds. We prove that a compact Kähler-like and G-Kähler-like almost Hermitian manifold equipped with an almost balanced metric is Kähler. We also show that if a Kähler-like and G-Kähler-like almost Hermitian manifold satisfies B_{\bar i\bar j}^\lambda B_{\lambda j}^i \ge 0, then the metric is almost balanced and the almost complex structure is integrable, which means that the metric is balanced. We investigate a G-Kähler-like almost Hermitian manifold under some assumptions.

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13

Bozzetti, Cristina, and Costantino Medori. "Almost complex manifolds with non-degenerate torsion." International Journal of Geometric Methods in Modern Physics 14, no. 03 (February 14, 2017): 1750033. http://dx.doi.org/10.1142/s0219887817500335.

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We show that almost complex manifolds [Formula: see text] of real dimension 4 for which the image of the Nijenhuis tensor forms a non-integrable bundle, called torsion bundle, admit a [Formula: see text]-structure locally, that is, a double absolute parallelism. In this way, the problem of equivalence for such almost complex manifolds can be solved; moreover, the classification of locally homogeneous manifold [Formula: see text] is explicitly given when the Lie algebra of its infinitesimal automorphisms is non-solvable (indeed reductive). It is also shown that the group of the automorphisms of [Formula: see text] is a Lie group of dimension less than or equal to 4, whose isotropy subgroup has at most two elements, and that there are not non-constant holomorphic functions on [Formula: see text].

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14

Manev, Mancho. "Yamabe Solitons on Conformal Almost-Contact Complex Riemannian Manifolds with Vertical Torse-Forming Vector Field." Axioms 12, no. 1 (January 1, 2023): 44. http://dx.doi.org/10.3390/axioms12010044.

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A Yamabe soliton is considered on an almost-contact complex Riemannian manifold (also known as an almost-contact B-metric manifold), which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. A case in which the potential is a torse-forming vector field of constant length on the vertical distribution determined by the Reeb vector field is studied. In this way, manifolds from one of the main classes of the studied manifolds are obtained. The same class contains the conformally equivalent manifolds of cosymplectic manifolds by the usual conformal transformation of the given B-metric. An explicit five-dimensional example of a Lie group is given, which is characterized in relation to the obtained results.

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15

Daurtseva, N. A. "On the Manifold of Almost Complex Structures." Mathematical Notes 78, no. 1-2 (July 2005): 59–63. http://dx.doi.org/10.1007/s11006-005-0099-7.

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16

PAK, HONG KYUNG. "TRANSVERSAL HARMONIC THEORY FOR TRANSVERSALLY SYMPLECTIC FLOWS." Journal of the Australian Mathematical Society 84, no. 2 (April 2008): 233–45. http://dx.doi.org/10.1017/s1446788708000190.

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AbstractWe develop the transversal harmonic theory for a transversally symplectic flow on a manifold and establish the transversal hard Lefschetz theorem. Our main results extend the cases for a contact manifold (H. Kitahara and H. K. Pak, ‘A note on harmonic forms on a compact manifold’, Kyungpook Math. J.43 (2003), 1–10) and for an almost cosymplectic manifold (R. Ibanez, ‘Harmonic cohomology classes of almost cosymplectic manifolds’, Michigan Math. J.44 (1997), 183–199). For the point foliation these are the results obtained by Brylinski (‘A differential complex for Poisson manifold’, J. Differential Geom.28 (1988), 93–114), Haller (‘Harmonic cohomology of symplectic manifolds’, Adv. Math.180 (2003), 87–103), Mathieu (‘Harmonic cohomology classes of symplectic manifolds’, Comment. Math. Helv.70 (1995), 1–9) and Yan (‘Hodge structure on symplectic manifolds’, Adv. Math.120 (1996), 143–154).

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17

Nazimuddin, AKM, and Md Showkat Ali. "Symplectic and Contact Geometry with Complex Manifolds." GANIT: Journal of Bangladesh Mathematical Society 39 (November 19, 2019): 119–26. http://dx.doi.org/10.3329/ganit.v39i0.44163.

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In this paper, we discuss about almost complex structures and complex structures on Riemannian manifolds, symplectic manifolds and contact manifolds. We have also shown a special comparison between complex symplectic geometry and complex contact geometry. Also, the existence of a complex submanifold of n-dimensional complex manifold which intersects a real submanifold GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 119-126

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18

Carmona Jiménez, José Luis, and Marco Castrillón López. "Reduction of Homogeneous Pseudo-Kähler Structures by One-Dimensional Fibers." Axioms 9, no. 3 (August 1, 2020): 94. http://dx.doi.org/10.3390/axioms9030094.

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We study the reduction procedure applied to pseudo-Kähler manifolds by a one dimensional Lie group acting by isometries and preserving the complex tensor. We endow the quotient manifold with an almost contact metric structure. We use this fact to connect pseudo-Kähler homogeneous structures with almost contact metric homogeneous structures. This relation will have consequences in the class of the almost contact manifold. Indeed, if we choose a pseudo-Kähler homogeneous structure of linear type, then the reduced, almost contact homogeneous structure is of linear type and the reduced manifold is of type C5⊕C6⊕C12 of Chinea-González classification.

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19

Milivojević, Aleksandar. "On the characterization of rational homotopy types and Chern classes of closed almost complex manifolds." Complex Manifolds 9, no. 1 (January 1, 2022): 138–69. http://dx.doi.org/10.1515/coma-2021-0133.

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Abstract We give an exposition of Sullivan’s theorem on realizing rational homotopy types by closed smooth manifolds, including a discussion of the necessary rational homotopy and surgery theory, adapted to the realization problem for almost complex manifolds: namely, we give a characterization of the possible simply connected rational homotopy types, along with a choice of rational Chern classes and fundamental class, realized by simply connected closed almost complex manifolds in real dimensions six and greater. As a consequence, beyond demonstrating that rational homotopy types of closed almost complex manifolds are plenty, we observe that the realizability of a simply connected rational homotopy type by a simply connected closed almost complex manifold depends only on its cohomology ring. We conclude with some computations and examples.

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20

Abbena, Elsa, and Sergio Garbiero. "Almost Hermitian homogeneous structures." Proceedings of the Edinburgh Mathematical Society 31, no. 3 (October 1988): 375–95. http://dx.doi.org/10.1017/s0013091500006775.

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Let (M, g, J) be an almost Hermitian manifold. More precisely, M is a ∞ differentiable manifold of dimension 2n, J is an almost complex structure on M, i.e. it is a tensor field of type (1, 1) such thatfor any X∈(M), ((M) is the Lie algebra of ∞ vector fields on M), and g is a Riemannian metric compatible with J, i.e.

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21

Schmidt, Benjamin, Krishnan Shankar, and Ralf Spatzier. "Almost isotropic Kähler manifolds." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 767 (October 1, 2020): 1–16. http://dx.doi.org/10.1515/crelle-2019-0030.

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AbstractLet M be a complete Riemannian manifold and suppose {p\in M}. For each unit vector {v\in T_{p}M}, the Jacobi operator, {\mathcal{J}_{v}:v^{\perp}\rightarrow v^{\perp}} is the symmetric endomorphism, {\mathcal{J}_{v}(w)=R(w,v)v}. Then p is an isotropic point if there exists a constant {\kappa_{p}\in{\mathbb{R}}} such that {\mathcal{J}_{v}=\kappa_{p}\operatorname{Id}_{v^{\perp}}} for each unit vector {v\in T_{p}M}. If all points are isotropic, then M is said to be isotropic; it is a classical result of Schur that isotropic manifolds of dimension at least 3 have constant sectional curvatures. In this paper we consider almost isotropic manifolds, i.e. manifolds having the property that for each {p\in M}, there exists a constant {\kappa_{p}\in\mathbb{R}} such that the Jacobi operators {\mathcal{J}_{v}} satisfy {\operatorname{rank}({\mathcal{J}_{v}-\kappa_{p}\operatorname{Id}_{v^{\perp}}}% )\leq 1} for each unit vector {v\in T_{p}M}. Our main theorem classifies the almost isotropic simply connected Kähler manifolds, proving that those of dimension {d=2n\geqslant 4} are either isometric to complex projective space or complex hyperbolic space or are totally geodesically foliated by leaves isometric to {{\mathbb{C}}^{n-1}}.

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22

Bejan, Cornelia-Livia, Şemsi Eken Meriç, and Erol Kılıç. "Contact-Complex Riemannian Submersions." Mathematics 9, no. 23 (November 23, 2021): 2996. http://dx.doi.org/10.3390/math9232996.

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A submersion from an almost contact Riemannian manifold to an almost Hermitian manifold, acting on the horizontal distribution by preserving both the metric and the structure, is, roughly speaking a contact-complex Riemannian submersion. This paper deals mainly with a contact-complex Riemannian submersion from an η-Ricci soliton; it studies when the base manifold is Einstein on one side and when the fibres are η-Einstein submanifolds on the other side. Some results concerning the potential are also obtained here.

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23

Lempert, László, and Róbert Szőke. "The Tangent Bundle of an Almost Complex Manifold." Canadian Mathematical Bulletin 44, no. 1 (March 1, 2001): 70–79. http://dx.doi.org/10.4153/cmb-2001-008-6.

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AbstractMotivated by deformation theory of holomorphic maps between almost complex manifolds we endow, in a natural way, the tangent bundle of an almost complexmanifold with an almost complex structure. We describe various properties of this structure.

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24

Tardini, Nicoletta, and Adriano Tomassini. "On the cohomology of almost-complex and symplectic manifolds and proper surjective maps." International Journal of Mathematics 27, no. 12 (November 2016): 1650103. http://dx.doi.org/10.1142/s0129167x16501032.

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Let [Formula: see text] be an almost-complex manifold. In [Comparing tamed and compatible symplectic cones and cohomological properties of almost-complex manifolds, Comm. Anal. Geom. 17 (2009) 651–683], Li and Zhang introduce [Formula: see text] as the cohomology subgroups of the [Formula: see text]th de Rham cohomology group formed by classes represented by real pure-type forms. Given a proper, surjective, pseudo-holomorphic map between two almost-complex manifolds, we study the relationship among such cohomology groups. Similar results are proven in the symplectic setting for the cohomology groups introduced in [Cohomology and Hodge Theory on Symplectic manifolds: I, J. Differ. Geom. 91(3) (2012) 383–416] by Tseng and Yau and a new characterization of the hard Lefschetz condition in dimension [Formula: see text] is provided.

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25

Tardini, Nicoletta, and Adriano Tomassini. "Almost-complex invariants of families of six-dimensional solvmanifolds." Complex Manifolds 9, no. 1 (January 1, 2022): 238–60. http://dx.doi.org/10.1515/coma-2021-0139.

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Abstract We compute almost-complex invariants h ∂ ¯ p , o h_{\bar \partial }^{p,o} , h D o l p , o h_{Dol}^{p,o} and almost-Hermitian invariants h δ ¯ p , o h_{\bar \delta }^{p,o} on families of almost-Kähler and almost-Hermitian 6-dimensional solvmanifolds. Finally, as a consequence of almost-Kähler identities we provide an obstruction to the existence of a compatible symplectic structure on a given compact almost-complex manifold. Notice that, when (X, J, g, ω) is a compact almost Hermitian manifold of real dimension greater than four, not much is known concerning the numbers h ∂ ¯ p , q h_{\bar \partial }^{p,q} .

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Sabatini, Silvia. "On the Chern numbers and the Hilbert polynomial of an almost complex manifold with a circle action." Communications in Contemporary Mathematics 19, no. 04 (April 25, 2017): 1750043. http://dx.doi.org/10.1142/s0219199717500432.

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Let [Formula: see text] be a compact, connected, almost complex manifold of dimension [Formula: see text] endowed with a [Formula: see text]-preserving circle action with isolated fixed points. In this paper, we analyze the “geography problem” for such manifolds, deriving equations relating the Chern numbers to the index [Formula: see text] of [Formula: see text]. We study the symmetries and zeros of the Hilbert polynomial, which imply many rigidity results for the Chern numbers when [Formula: see text]. We apply these results to the category of compact, connected symplectic manifolds. A long-standing question posed by McDuff and Salamon asked about the existence of non-Hamiltonian actions with isolated fixed points. This question was answered recently by Tolman, with an explicit construction of a 6-dimensional manifold with such an action. One issue that this raises is whether one can find topological criteria that ensure the manifold can only support a Hamiltonian or only a non-Hamiltonian action. In this vein, we are able to deduce such criteria from our rigidity theorems in terms of relatively few Chern numbers, depending on the index. Another consequence is that, if the action is Hamiltonian, the minimal Chern number coincides with the index and is at most [Formula: see text].

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Ermolitski, Alexander A. "Embeddings of Almost Hermitian Manifold in Almost Hyper Hermitian Manifold and Complex (Hypercomplex) Numbers in Riemannian Geometry." Applied Mathematics 05, no. 16 (2014): 2464–75. http://dx.doi.org/10.4236/am.2014.516238.

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28

Alghanemi, Azeb, Noura Al-houiti, Bang-Yen Chen, and Siraj Uddin. "Existence and uniqueness theorems for pointwise slant immersions in complex space forms." Filomat 35, no. 9 (2021): 3127–38. http://dx.doi.org/10.2298/fil2109127a.

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An isometric immersion f : Mn ? ?Mm from an n-dimensional Riemannian manifold Mn into an almost Hermitian manifold ?Mm of complex dimension m is called pointwise slant if its Wirtinger angles define a function defined on Mn. In this paper we establish the Existence and Uniqueness Theorems for pointwise slant immersions of Riemannian manifolds Mn into a complex space form ?Mn(c) of constant holomorphic sectional curvature c, which extend the Existence and Uniqueness Theorems for slant immersions proved by B.-Y. Chen and L. Vrancken in 1997.

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Solgun, Mehmet. "On constructing almost complex Norden metric structures." AIMS Mathematics 7, no. 10 (2022): 17942–53. http://dx.doi.org/10.3934/math.2022988.

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<abstract><p>For a given almost contact Norden metric structure on a smooth manifold $ M $, one can obtain an almost complex Norden metric structure on $ M\times\mathbb{R} $. In this work, we study this construction in details and give the relations between the classes of these structures. Furthermore, we give examples of almost complex Norden metric structures of which the existence are guaranteed by the results of the paper.</p></abstract>

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SALAVESSA, ISABEL M. C., and ANA PEREIRA DO VALE. "TRANSGRESSION FORMS IN DIMENSION 4." International Journal of Geometric Methods in Modern Physics 03, no. 05n06 (September 2006): 1221–54. http://dx.doi.org/10.1142/s0219887806001442.

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We compute explicit transgression forms for the Euler and Pontrjagin classes of a Riemannian manifold M of dimension 4 under a conformal change of the metric, or a change to a Riemannian connection with torsion. These formulas describe the singular set of some connections with singularities on compact manifolds as a residue formula in terms of a polynomial of invariants. We give some applications for minimal submanifolds of Kähler manifolds. We also express the difference of the first Chern class of two almost complex structures, and in particular an obstruction to the existence of a homotopy between them, by a residue formula along the set of anti-complex points. Finally we take the first steps in the study of obstructions for two almost quaternionic-Hermitian structures on a manifold of dimension 8 to have homotopic fundamental forms or isomorphic twistor spaces.

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Datar, Ved, Harish Seshadri, and Jian Song. "Metric rigidity of Kähler manifolds with lower Ricci bounds and almost maximal volume." Proceedings of the American Mathematical Society 149, no. 8 (May 18, 2021): 3569–74. http://dx.doi.org/10.1090/proc/15473.

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In this short note we prove that a Kähler manifold with lower Ricci curvature bound and almost maximal volume is Gromov-Hausdorff close to the projective space with the Fubini-Study metric. This is done by combining the recent results on holomorphic rigidity of such Kähler manifolds (see Gang Liu [Asian J. Math. 18 (2014), 69–99]) with the structure theorem of Tian-Wang (see Gang Tian and Bing Wang [J. Amer. Math. Soc 28 (2015), 1169–1209]) for almost Einstein manifolds. This can be regarded as the complex analog of the result on Colding on the shape of Riemannian manifolds with almost maximal volume.

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Yang, Kichoon. "Almost complex structures on the orthogonal twistor bundle." Bulletin of the Australian Mathematical Society 40, no. 3 (December 1989): 337–44. http://dx.doi.org/10.1017/s0004972700017354.

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We give a construction of 2s, s = n(n – 1)/2, many natural almost complex structures on the orthogonal twistor bundle over a 2n-dimensional Riemannian manifold. The usual almost complex structures are then characterised by the condition that they correspond to integrable invariant complex structures on the standard fibre which is identified with the hermitian symmetric space SO(2n)/U(n).

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Bonome, A., R. Castro, and L. M. Hervella. "Almost complex structure in the frame bundle of an almost contact metric manifold." Mathematische Zeitschrift 193, no. 3 (September 1986): 431–40. http://dx.doi.org/10.1007/bf01229810.

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Tosatti, Valentino, and Ben Weinkove. "The Calabi–Yau equation on the Kodaira–Thurston manifold." Journal of the Institute of Mathematics of Jussieu 10, no. 2 (September 24, 2010): 437–47. http://dx.doi.org/10.1017/s1474748010000289.

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AbstractWe prove that the Calabi–Yau equation can be solved on the Kodaira–Thurston manifold for all given T2-invariant volume forms. This provides support for Donaldson's conjecture that Yau's theorem has an extension to symplectic 4-manifolds with compatible but non-integrable almost complex structures.

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LEE, JUNG CHAN, JEONG HYEONG PARK, and KOUEI SEKIGAWA. "CRITICAL HERMITIAN STRUCTURES ON THE PRODUCT OF SASAKIAN MANIFOLDS." International Journal of Geometric Methods in Modern Physics 09, no. 07 (September 7, 2012): 1250055. http://dx.doi.org/10.1142/s0219887812500557.

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Let [Formula: see text] be a compact orientable smooth manifold admitting an almost complex structure and [Formula: see text] for (λ, μ) ∈ ℝ2 - (0, 0) be the functional defined on the space of the almost Hermitian structure [Formula: see text]. We discuss the first variational problem of the functional [Formula: see text] on the space [Formula: see text] and its subspace [Formula: see text] in the case where [Formula: see text] is a product manifold of Sasakian manifolds. Further this paper provides examples of critical Hermitian structures of the functional [Formula: see text] for various (λ, μ).

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36

Ali, Danish, Johann Davidov, and Oleg Mushkarov. "Holomorphic curvatures of twistor spaces." International Journal of Geometric Methods in Modern Physics 11, no. 03 (March 2014): 1450022. http://dx.doi.org/10.1142/s0219887814500224.

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We study the twistor spaces of oriented Riemannian 4-manifolds as a source of almost Hermitian 6-manifolds of constant or strictly positive holomorphic, Hermitian and orthogonal bisectional curvatures. In particular, we obtain explicit formulas for these curvatures in the case when the base manifold is Einstein and self-dual, and observe that the "squashed" metric on ℂℙ3 is a non-Kähler Hermitian–Einstein metric of positive holomorphic bisectional curvature. This shows that a recent result of Kalafat and Koca [M. Kalafat and C. Koca, Einstein–Hermitian 4-manifolds of positive bisectional curvature, preprint (2012), arXiv: 1206.3941v1 [math.DG]] in dimension four cannot be extended to higher dimensions. We prove that the Hermitian bisectional curvature of a non-Kähler Hermitian manifold is never a nonzero constant which gives a partial negative answer to a question of Balas and Gauduchon [A. Balas and P. Gauduchon, Any Hermitian metric of constant non-positive (Hermitian) holomorphic sectional curvature on a compact complex surface is Kähler, Math. Z.190 (1985) 39–43]. Finally, motivated by an integrability result of Vezzoni [L. Vezzoni, On the Hermitian curvature of symplectic manifolds, Adv. Geom.7 (2007) 207–214] for almost Kähler manifolds, we study the problem when the holomorphic and the Hermitian bisectional curvatures of an almost Hermitian manifold coincide. We extend the result of Vezzoni to a more general class of almost Hermitian manifolds and describe the twistor spaces having this curvature property.

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37

Isidro, José M. "Duality, Quantum Mechanics and (Almost) Complex Manifolds." Modern Physics Letters A 18, no. 28 (September 14, 2003): 1975–90. http://dx.doi.org/10.1142/s0217732303011873.

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The classical mechanics of a finite number of degrees of freedom requires a symplectic structure on phase space [Formula: see text], but it is independent of any complex structure. On the contrary, the quantum theory is intimately linked with the choice of a complex structure on [Formula: see text]. When the latter is a complex-analytic manifold admitting just one complex structure, there is a unique quantization whose classical limit is [Formula: see text]. Then the notion of coherence is the same for all observers. However, when [Formula: see text] admits two or more nonbiholomorphic complex structures, there is one different quantization per different complex structure on [Formula: see text]. The lack of analyticity in transforming between nonbiholomorphic complex structures can be interpreted as the loss of quantum-mechanical coherence under the corresponding transformation. Observers using one complex structure perceive as coherent the states that other observers, using a different complex structure, do not perceive as such. This is the notion of a quantum-mechanical duality transformation: the relativity of the notion of a quantum.

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38

SUKHOV, ALEXANDRE. "REGULARIZED MAXIMUM OF STRICTLY PLURISUBHARMONIC FUNCTIONS ON AN ALMOST COMPLEX MANIFOLD." International Journal of Mathematics 24, no. 12 (November 2013): 1350097. http://dx.doi.org/10.1142/s0129167x13500973.

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39

Foth, T., and A. Uribe. "The Manifold of Compatible Almost Complex Structures and Geometric Quantization." Communications in Mathematical Physics 274, no. 2 (June 23, 2007): 357–79. http://dx.doi.org/10.1007/s00220-007-0280-9.

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40

Gao, Hongzhu. "Anti-holomorphic involutions and almost complex structures on four-manifold." Science in China Series A: Mathematics 42, no. 6 (June 1989): 586–92. http://dx.doi.org/10.1007/bf02880076.

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41

Gulbahar, Mehmet, Erol Kilic, and Sadik Keles. "A useful orthonormal basis on bi-slant submanifolds of almost Hermitian manifolds." Tamkang Journal of Mathematics 47, no. 2 (June 30, 2016): 143–61. http://dx.doi.org/10.5556/j.tkjm.47.2016.1748.

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In this paper, we study bi-slant submanifolds of an almost Hermitian manifold for different cases. We introduce a new orthonormal basis on bi-slant submanifold, semi-slant submanifold and hemi-slant submanifold of an almost Hermitian manifold to compute Chen's main inequalities. We investigate these inequalities for semi-slant submanifolds, hemi-slant submanifolds and slant submanifolds of a generalized complex space form. We obtain some characterizations on such submanifolds of a complex space form.

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42

Baghban, Amir, and Esmaeil Abedi. "A new class of almost complex structures on tangent bundle of a Riemannian manifold." Communications in Mathematics 26, no. 2 (December 1, 2018): 137–45. http://dx.doi.org/10.2478/cm-2018-0010.

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AbstractIn this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced (0, 2)-tensor on the tangent bundle using these structures and Liouville 1-form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

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43

Davidov, Johann, Absar Ul-Haq, and Oleg Mushkarov. "Harmonicity of proper almost complex structures on Walker 4-manifolds." International Journal of Geometric Methods in Modern Physics 14, no. 06 (May 4, 2017): 1750094. http://dx.doi.org/10.1142/s0219887817500943.

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Every Walker [Formula: see text]-manifold [Formula: see text], endowed with a canonical neutral metric [Formula: see text], admits a specific almost complex structure called proper. In this paper, we find the conditions under which a proper almost complex structure is a harmonic section or a harmonic map from [Formula: see text] to its hyperbolic twistor space.

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SPIRO, ANDREA. "TOTAL REALITY OF CONORMAL BUNDLES OF HYPERSURFACES IN ALMOST COMPLEX MANIFOLDS." International Journal of Geometric Methods in Modern Physics 03, no. 05n06 (September 2006): 1255–62. http://dx.doi.org/10.1142/s0219887806001454.

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A generalization to the almost complex setting of a well-known result by Webster is given. Namely, we prove that if Γ is a strongly pseudoconvex hypersurface in an almost complex manifold (M, J), then the conormal bundle of Γ is a totally real submanifold of (T* M, 𝕁), where 𝕁 is the lifted almost complex structure on T* M defined by Ishihara and Yano.

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Ishikawa, Goo, and Toru Ohmoto. "Local invariants of singular surfaces in an almost complex four-manifold." Annals of Global Analysis and Geometry 11, no. 2 (May 1993): 125–33. http://dx.doi.org/10.1007/bf00773451.

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Schäfer, Lars. "tt∗-geometry on the tangent bundle of an almost complex manifold." Journal of Geometry and Physics 57, no. 3 (February 2007): 999–1014. http://dx.doi.org/10.1016/j.geomphys.2006.08.004.

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SALIMOV, A. A. "A NOTE ON THE GOLDBERG CONJECTURE OF WALKER MANIFOLDS." International Journal of Geometric Methods in Modern Physics 08, no. 05 (August 2011): 925–28. http://dx.doi.org/10.1142/s021988781100549x.

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This paper is concerned with Goldberg conjecture. Using the ϕφ-operator we prove the following result. Let (M, φ, w g) be an almost Kähler–Walker–Einstein compact manifold with the proper almost complex structure φ. The proper almost complex structure φ on Walker manifold (M, w g) is integrable if ϕφgN+ = 0, where gN+ is the induced Norden–Walker metric on M. This resolves a conjecture of Goldberg under the additional restriction on Norden–Walker metric (gN+ ∈ Ker ϕφ).

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48

Cho, Jong Taek, and Makoto Kimura. "Transversal Jacobi Operators in Almost Contact Manifolds." Mathematics 9, no. 1 (December 24, 2020): 31. http://dx.doi.org/10.3390/math9010031.

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Along a transversal geodesic γ whose tangent belongs to the contact distribution D, we define the transversal Jacobi operator Rγ=R(·,γ˙)γ˙ on an almost contact Riemannian manifold M. Then, using the transversal Jacobi operator Rγ, we give a new characterization of the Sasakian sphere. In the second part, we characterize the complete ruled real hypersurfaces in complex hyperbolic space.

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KON, S. H., and SIN-LENG TAN. "CR-SUBMANIFOLDS OF A QUASl-KAEHLER MANIFOLD." Tamkang Journal of Mathematics 26, no. 3 (September 1, 1995): 261–66. http://dx.doi.org/10.5556/j.tkjm.26.1995.4405.

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Let $M$ be a CR-submanifold of a quasi-Kaehler manifold $N$. Sufficient conditions for the holomorphic distribution $D$ in $M$ to be integrable are derived. We also show that $D$ is minimal. It follows that an (almost) complex submanifold of a quasi-Kaehler manifold is minimal, this generalizes the well known result that a complex submanifold of a Kaehler manifold is minimal.

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GAUSSIER, HERVÉ, and KANG-TAE KIM. "COMPACTNESS OF CERTAIN FAMILIES OF PSEUDO-HOLOMORPHIC MAPPINGS INTO ${\mathbb C}^n$." International Journal of Mathematics 15, no. 01 (February 2004): 1–12. http://dx.doi.org/10.1142/s0129167x04002168.

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We present a normal family theorem for injective almost holomorphic maps from a manifold with almost complex structures into [Formula: see text]. Our theorem implies a new consequence even for the holomorphic mappings of a complex manifold into [Formula: see text], which can be seen as a generalization of the convergence theorem for Frankel's scaling sequence whose images are not necessarily convex. Moreover, our method is closer in spirit to the circle of ideas centered around the classical Montel theorem.

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