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Journal articles on the topic 'Foliation'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Zhukova, N. I., G. S. Levin, and N. S. Tonysheva. "Chaos in Topological Foliations." Contemporary Mathematics. Fundamental Directions 68, no. 3 (2022): 424–50. http://dx.doi.org/10.22363/2413-3639-2022-68-3-424-450.

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We call a foliation (M,F) on a manifold M chaotic if it is topologically transitive and the union of closed leaves is dense in M. A foliated manifold M is not assumed to be compact. The chaotic foliations can be considered as multidimensional generalization of chaotic dynamical systems in the sense of Devaney. For foliations covered by fibrations we prove that a foliation is chaotic if and only if its global holonomy group is chaotic. We introduce the concept of the integrable Ehresmann connection for a foliation as a natural generalization of the integrable Ehresmann connection for smooth fol

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2

Zhukova, N. I. "Riemannian foliations with Ehresmann connection." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 20, no. 4 (2018): 395–407. http://dx.doi.org/10.15507/2079-6900.20.201804.395-407.

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It is shown that the structural theory of Molino for Riemannian foliations on compact manifolds and complete Riemannian manifolds may be generalized to a Riemannian foliations with Ehresmann connection. Within this generalization there are no restrictions on the codimension of the foliation and on the dimension of the foliated manifold. For a Riemannian foliation (M,F) with Ehresmann connection it is proved that the closure of any leaf forms a minimal set, the family of all such closures forms a singular Riemannian foliation (M,F¯¯¯¯). It is shown that in M there exists a connected open dense

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3

Shanti Caillat-Gibert and Daniel Matignon. "Existence of Taut Foliations on Seifert Fibered Homology 3-spheres." Canadian Journal of Mathematics 66, no. 1 (2014): 141–69. http://dx.doi.org/10.4153/cjm-2013-011-4.

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AbstractThis paper concerns the problem of existence of taut foliations among 3-manifolds. From the work of David Gabai we know that a closed 3-manifold with non-trivial second homology group admits a taut foliation. The essential part of this paper focuses on Seifert fibered homology 3-spheres. The result is quite different if they are integral or rational but non-integral homology 3-spheres. Concerning integral homology 3-spheres, we can see that all but the 3-sphere and the Poincaré 3-sphere admit a taut foliation. Concerning non-integral homology 3-spheres, we prove there are infinitely ma

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4

Mori, Atsuhide. "A Note on Mitsumatsu’s Construction of a Leafwise Symplectic Foliation." International Mathematics Research Notices 2019, no. 22 (2017): 6933–48. http://dx.doi.org/10.1093/imrn/rnx321.

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Abstract Mitsumatsu [9] constructed a leafwise symplectic structure of the Lawson foliation of S5. Following his construction, we improve a previous result of the author [11] on convergence of contact structure to codimension one foliation, and give a sufficient condition for convergence to foliation with leafwise symplectic structure. As an application, we show that the product S4 × S1 admits infinitely many codimension one leafwise symplectic foliations.

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5

Alaoui, Aziz El Kacimi, and Marcel Nicolau. "A class of C∞-stable foliations." Ergodic Theory and Dynamical Systems 13, no. 4 (1993): 697–704. http://dx.doi.org/10.1017/s0143385700007628.

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AbstractWe consider foliations F obtained as the suspension of a linear foliation F0 on n by means of a linear Anosov diffeomorphism A of n keeping F0 invariant. Under suitable conditions on A the foliations F are shown to be C∞-stable, i.e. any differentiable foliation which is C∞-close to F is C∞-conjugated to F. The proof relies on a criterium of stability stated by R. Hamilton.

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6

Brunella, Marco. "Remarks on structurally stable proper foliations." Mathematical Proceedings of the Cambridge Philosophical Society 115, no. 1 (1994): 111–20. http://dx.doi.org/10.1017/s0305004100071954.

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Let M be a closed manifold of dimension 3 and let Fol(M) be the space of codimension one C∞-foliations on M. A foliation ∈ Fol(M) is said to be Cr- structurally stable if there exists a neighbourhood V of in Fol(M) in the (Epstein) Cr-topology such that every foliation is topologically conjugate to , through a homeomorphism near to the identity. Some background on the problem of structural stability of foliations can be found in [8]. In this paper we shall be concerned with proper foliations, i.e. foliations all of whose leaves are proper.

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QADIR, ASGHAR, and AZAD A. SIDDIQUI. "FOLIATION OF THE SCHWARZSCHILD AND REISSNER–NORDSTRÖM SPACE–TIMES BY FLAT SPACE-LIKE HYPERSURFACES." International Journal of Modern Physics D 15, no. 09 (2006): 1419–40. http://dx.doi.org/10.1142/s0218271806009157.

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It is known that spherically symmetric space–times admit flat space-like foliations. In this paper a simple procedure for the complete foliation of the Schwarzschild space–time by flat space-like hypersurfaces is developed, using the fact that unforced geodesics are orthogonal to such hypersurfaces. The method is then extended to obtain a complete foliation of the Reissner–Nordström space–time by such hypersurfaces. In this case, as there is a barrier beyond which the geodesics do not go, a complete foliation is obtained by analytically continuing the hypersurfaces beyond the barrier. A dualit

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8

Barbot, Thierry. "Caractérisation des flots d' Anosov en dimension 3 par leurs feuilletages faibles." Ergodic Theory and Dynamical Systems 15, no. 2 (1995): 247–70. http://dx.doi.org/10.1017/s0143385700008361.

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AbstractWe consider Anosov flows on closed 3-manifolds. We show that if such a flow admits a weak foliation whose lifting in the universal covering is a product foliation, thenit is characterized up to topological equivalence by its weak stable foliation up to topological conjugacy. As a corollary we obtain that, up to topological equivalence and finite coverings, suspensions and geodesic flows are the unique Anosov flows on closed 3-manifolds whose weak stable foliations are transversely projective.

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9

Hwang, Jun-Muk, and Eckart Viehweg. "Characteristic foliation on a hypersurface of general type in a projective symplectic manifold." Compositio Mathematica 146, no. 2 (2010): 497–506. http://dx.doi.org/10.1112/s0010437x09004412.

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AbstractA foliation on a non-singular projective variety is algebraically integrable if all leaves are algebraic subvarieties. A non-singular hypersurface X in a non-singular projective variety M equipped with a symplectic form has a naturally defined foliation, called the characteristic foliation on X. We show that if X is of general type and dim M≥4, then the characteristic foliation on X cannot be algebraically integrable. This is a consequence of a more general result on Iitaka dimensions of certain invertible sheaves associated with algebraically integrable foliations by curves. The latte

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10

Deroin, Bertrand, and Adolfo Guillot. "Foliated affine and projective structures." Compositio Mathematica 159, no. 6 (2023): 1153–87. http://dx.doi.org/10.1112/s0010437x2300711x.

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We formalize the concepts of holomorphic affine and projective structures along the leaves of holomorphic foliations by curves on complex manifolds. We show that many foliations admit such structures, we provide local normal forms for them at singular points of the foliation, and we prove some index formulae in the case where the ambient manifold is compact. As a consequence of these, we establish that a regular foliation of general type on a compact algebraic manifold of even dimension does not admit a foliated projective structure. Finally, we classify foliated affine and projective structur

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11

AZEVEDO SCÁRDUA, B. C., and J. C. CANILLE MARTINS. "ON THE GROWTH OF HOLOMORPHIC PROJECTIVE FOLIATIONS." International Journal of Mathematics 13, no. 07 (2002): 695–726. http://dx.doi.org/10.1142/s0129167x02001502.

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In the theory of real (non-singular) foliations, the study of the growth of the leaves has proved to be useful in the comprehension of the global dynamics as the existence of compact leaves and exceptional minimal sets. In this paper we are interested in the complex version of some of these basic results. A natural question is the following: What can be said of a codimension one (possibly singular) holomorphic foliation on a compact hermitian manifold M exhibiting subexponential growth for the leaves? One of the first examples comes when we consider the Fubini–Study metric on [Formula: see tex

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12

Mol, Rogério S. "Flags of holomorphic foliations." Anais da Academia Brasileira de Ciências 83, no. 3 (2011): 775–86. http://dx.doi.org/10.1590/s0001-37652011005000025.

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A flag of holomorphic foliations on a complex manifold M is an object consisting of a finite number of singular holomorphic foliations on M of growing dimensions such that the tangent sheaf of a fixed foliation is a subsheaf of the tangent sheaf of any of the foliations of higher dimension. We study some basic properties oft hese objects and, in <img src="/img/revistas/aabc/2011nahead/aop2411pcn.jpg" align="absmiddle" />, n > 3, we establish some necessary conditions for a foliation, we find bounds of lower dimension to leave invariant foliations of codimension one. Finally, still in

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13

Biswas, Indranil. "Generalized transversely projective structure on a transversely holomorphic foliation." International Journal of Mathematics and Mathematical Sciences 30, no. 3 (2002): 151–63. http://dx.doi.org/10.1155/s016117120201116x.

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The results of Biswas (2000) are extended to the situation of transversely projective foliations. In particular, it is shown that a transversely holomorphic foliation defined using everywhere locally nondegenerate maps to a projective spaceℂℙn, and whose transition functions are given by automorphisms of the projective space, has a canonical transversely projective structure. Such a foliation is also associated with a transversely holomorphic section ofN⊗−kfor eachk∈[3,n+1], whereNis the normal bundle to the foliation. These transversely holomorphic sections are also flat with respect to the B

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14

Zhang, Qunlei, Zihan Zhi, Chun Feng, Ruixia Li, Jinchao Yue, and Junyu Cong. "Using Continuum-Discontinuum Element Method to Model the Foliation-Affected Fracturing in Rock Brazilian Test." Advances in Civil Engineering 2021 (July 6, 2021): 1–9. http://dx.doi.org/10.1155/2021/1404568.

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In this study, the continuum-discontinuum element method (CDEM) was used to investigate the tensile fracture mechanism of rock materials. An isotropic rock disk model and models considering different foliation inclinations were established, and three schemes were used to simulate the rock fracturing in Brazilian test. Then, the influences of the rock matrix and foliation strengths on anisotropy rock fracturing were investigated. Furtherly, simulation results were verified, and the rock fracture mechanisms were discussed. The results show that the rock fracturing in Brazilian test can be accura

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15

EGASHIRA, SHINJI. "Qualitative theory and expansion growth of transversely piecewise-smooth foliated ${S}^{1}$-bundles." Ergodic Theory and Dynamical Systems 17, no. 2 (1997): 331–47. http://dx.doi.org/10.1017/s0143385797079157.

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We study a qualitative theory of compact, transversely piecewise-smooth foliated $S^1$-bundles. We show that it has the same qualitative properties as that of smooth codimension-one foliations on a compact manifold. By the obtained qualitative properties, we can deduce that the expansion growth of this foliation is classified and that the entropy of this foliation is positive if and only if there exists a resilient leaf.

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16

Rovenski, Vladimir. "Integral Formulas for a Foliation with a Unit Normal Vector Field." Mathematics 9, no. 15 (2021): 1764. http://dx.doi.org/10.3390/math9151764.

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In this article, we prove integral formulas for a Riemannian manifold equipped with a foliation F and a unit vector field N orthogonal to F, and generalize known integral formulas (due to Brito-Langevin-Rosenberg and Andrzejewski-Walczak) for foliations of codimension one. Our integral formulas involve Newton transformations of the shape operator of F with respect to N and the curvature tensor of the induced connection on the distribution D=TF⊕span(N), and this decomposition of D can be regarded as a codimension-one foliation of a sub-Riemannian manifold. We apply our formulas to foliated (sub

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17

Park, Kyewon. "On ergodic foliations." Ergodic Theory and Dynamical Systems 8, no. 3 (1988): 437–57. http://dx.doi.org/10.1017/s0143385700004570.

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AbstractWe define an ergodic ℤ-foliation and show that it can be realized as a quotient space of the ‘covering space’. The covering space has two actions, T and S, where T is a ℤ-action, S is a map of order two, and S and T skew-commute; that is, STS = T−1. We study the isometry between two foliations via the isomorphism between two bigger group actions in the covering spaces. Properties of an ergodic foliation are studied in a way similar to the study of an ergodic action. We construct a counterexample of a K-automorphism to show that, unlike Bernoulli automorphisms, ℤ-actions do not complete

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18

Mourier, Pierre, and Asta Heinesen. "Splitting the spacetime: a systematic analysis of foliation dependence in cosmic averaging." Journal of Cosmology and Astroparticle Physics 2024, no. 04 (2024): 067. http://dx.doi.org/10.1088/1475-7516/2024/04/067.

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Abstract It is a fundamental unsolved question in general relativity how to unambiguously characterize the effective collective dynamics of an ensemble of fluid elements sourcing the local geometry, in the absence of exact symmetries. In a cosmological context this is sometimes referred to as the averaging problem. At the heart of this problem in relativity is the non-uniqueness of the choice of foliation within which the statistical properties of the local spacetime are quantified, which can lead to ambiguity in the formulated average theory. This has led to debate in the literature on how to

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19

GOLENISHCHEVA-KUTUZOVA, T., та V. KLEPTSYN. "Minimality and ergodicity of a generic analytic foliation of ℂ2". Ergodic Theory and Dynamical Systems 28, № 5 (2008): 1533–44. http://dx.doi.org/10.1017/s0143385707000934.

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20

Maksymenko, Sergiy. "Diffeomorphism groups of Morse-Bott foliation on the solid Klein bottle by Klein bottles parallel to the boundary." Збірник Праць Інституту математики НАН України 20, no. 1 (2023): 896–910. http://dx.doi.org/10.3842/trim.v20n1.532.

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Let $\mathcal{G}$ be a Morse-Bott foliation on the solid Klein bottle $\mathbf{K}$ into $2$-dimensional Klein bottles parallel to the boundary and one singular circle $S^1$. Let also $S^1\widetilde{\times}S^2$ be the twisted bundle over $S^1$ which is a union of two solid Klein bottles $\mathbf{K}_0$ and $\mathbf{K}_1$ with common boundary $K$. Then the above foliation $\mathcal{G}$ on both $\mathbf{K}_0$ and $\mathbf{K}_1$ gives a foliation $\mathcal{G}'$ on $S^1\widetilde{\times}S^2$ into parallel Klein bottles and two singluar circles. The paper computes the homotopy types of groups of foli

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21

MARTIN, REINER. "Non-uniquely ergodic foliations of thin type." Ergodic Theory and Dynamical Systems 17, no. 3 (1997): 667–74. http://dx.doi.org/10.1017/s0143385797079169.

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22

Fernández-Sánchez, Percy, Evelia R. García García Barroso, and Nancy Saravia-Molina. "On the Approximate Polar Curves of Foliations." Mathematics 11, no. 3 (2023): 613. http://dx.doi.org/10.3390/math11030613.

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We present a decomposition theorem of the generic polar curves of a generalized curve foliation with only one separatrix and the Hamiltonian foliations defined by the approximate roots of the generatrix. This is a generalization to foliations of the decomposition theorem of approximate Jacobians given by García Barroso and Gwoździewicz for plane branches.

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23

Blixt, Daniel, Alejandro Jiménez Cano, and Aneta Wojnar. "Foliation-Generating Observers under Lorentz Transformations." Symmetry 16, no. 10 (2024): 1384. http://dx.doi.org/10.3390/sym16101384.

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In this work, we revise the concept of foliation and related aspects that are crucial when formulating the Hamiltonian evolution for various theories beyond General Relativity. In particular, we show the relation between the kinematic characteristics of timelike congruences (observers) and the existence of foliations orthogonal to them. We then explore how local Lorentz transformations acting on observers affect the existence of transversal foliations, provide examples, and discuss the implications of these results for the 3+1 formulation of tetrad modified theories of gravity.

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24

Galindo, Carlos, Francisco Monserrat, and Jorge Olivares. "Foliations with isolated singularities on Hirzebruch surfaces." Forum Mathematicum 33, no. 6 (2021): 1471–86. http://dx.doi.org/10.1515/forum-2021-0135.

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Abstract We study foliations ℱ {\mathcal{F}} on Hirzebruch surfaces S δ {S_{\delta}} and prove that, similarly to those on the projective plane, any ℱ {\mathcal{F}} can be represented by a bi-homogeneous polynomial affine 1-form. In case ℱ {\mathcal{F}} has isolated singularities, we show that, for δ = 1 {\delta=1} , the singular scheme of ℱ {\mathcal{F}} does determine the foliation, with some exceptions that we describe, as is the case of foliations in the projective plane. For δ ≠ 1 {\delta\neq 1} , we prove that the singular scheme of ℱ {\mathcal{F}} does not determine the foliation. Howev

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25

Wolak, Robert A. "Closure of Leaves in Transversely Affine Foliations." Canadian Mathematical Bulletin 34, no. 4 (1991): 553–58. http://dx.doi.org/10.4153/cmb-1991-087-8.

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AbstractWe present first examples of complete transversely affine foliations on compact manifolds with leaves whose closures are not submanifolds. Moreover, we prove that under some additional assumptions the closures of leaves form a singular foliation.

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Suhr, Günter, Tom Calon, and Sherry M. Dunsworth. "Origin of complex upper mantle structures in the southern Lewis Hills (Bay of Islands Ophiolite, Newfoundland)." Canadian Journal of Earth Sciences 28, no. 5 (1991): 774–87. http://dx.doi.org/10.1139/e91-067.

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The Springers Hill area (Lewis Hills, Bay of Islands Ophiolite) may represent oceanic lithosphere created in close proximity to the nontransform segment of an oceanic fracture zone. Upper mantle rocks exposed on Springers Hill were investigated to establish whether their development was affected by the thermal and rheological changes associated with oceanic fracture zones. Harzburgites of the Springers Hill area reveal complex structural patterns. On a small scale, foliations defined by orthopyroxene grains intersect foliations defined by spinel grains at various angles. Olivine petrofabric wo

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27

Shi, Yi. "The dual foliation of some singular Riemannian foliations." Differential Geometry and its Applications 51 (April 2017): 9–14. http://dx.doi.org/10.1016/j.difgeo.2016.12.002.

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28

Leininger, Christopher, Anna Lenzhen, and Kasra Rafi. "Limit sets of Teichmüller geodesics with minimal non-uniquely ergodic vertical foliation." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 737 (2018): 1–32. http://dx.doi.org/10.1515/crelle-2015-0040.

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AbstractWe describe a method for constructing Teichmüller geodesics where the vertical foliation ν is minimal but is not uniquely ergodic and where we have a good understanding of the behavior of the Teichmüller geodesic. The construction depends on various parameters, and we show that one can adjust the parameters to ensure that the set of accumulation points of such a geodesic in the Thurston boundary is exactly the projective 1-simplex of all projective measured foliations that are topologically equivalent to ν. With further adjustment of the parameters, one can further assume that the tran

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HUA, YONGXIA, RADU SAGHIN, and ZHIHONG XIA. "Topological entropy and partially hyperbolic diffeomorphisms." Ergodic Theory and Dynamical Systems 28, no. 3 (2008): 843–62. http://dx.doi.org/10.1017/s0143385707000405.

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AbstractWe consider partially hyperbolic diffeomorphisms on compact manifolds. We define the notion of the unstable and stable foliations stably carrying some unique non-trivial homologies. Under this topological assumption, we prove the following two results: if the center foliation is one-dimensional, then the topological entropy is locally a constant; and if the center foliation is two-dimensional, then the topological entropy is continuous on the set of all $C^{\infty }$ diffeomorphisms. The proof uses a topological invariant we introduced, Yomdin’s theorem on upper semi-continuity, Katok’

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Hammerlindl, Andy. "Quasi-isometry and Plaque Expansiveness." Canadian Mathematical Bulletin 54, no. 4 (2011): 676–79. http://dx.doi.org/10.4153/cmb-2011-024-7.

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AbstractWe show that a partially hyperbolic diffeomorphism is plaque expansive (a form of structural stability for its center foliation) if the strong stable and unstable foliations are quasi-isometric in the universal cover. In particular, all partially hyperbolic diffeomorphisms on the 3-torus are plaque expansive.

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Mattei, J. F., J. C. Rebelo, and H. Reis. "Generic pseudogroups on and the topology of leaves." Compositio Mathematica 149, no. 8 (2013): 1401–30. http://dx.doi.org/10.1112/s0010437x13007161.

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AbstractWe show that generically a pseudogroup generated by holomorphic diffeomorphisms defined about $0\in \mathbb{C} $ is free in the sense of pseudogroups even if the class of conjugacy of the generators is fixed. This result has a number of consequences on the topology of leaves for a (singular) holomorphic foliation defined on a neighborhood of an invariant curve. In particular, in the classical and simplest case arising from local nilpotent foliations possessing a unique separatrix which is given by a cusp of the form $\{ {y}^{2} - {x}^{2n+ 1} = 0\} $, our results allow us to settle the

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Burelle, Jean-Philippe, and Dominik Francoeur. "Foliations between crooked planes in 3-dimensional Minkowski space." International Journal of Mathematics 30, no. 01 (2019): 1950004. http://dx.doi.org/10.1142/s0129167x19500046.

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We show that any two disjoint crooked planes in [Formula: see text] are leaves of a crooked foliation. This answers a question asked by Charette and Kim [V. Charette and Y. Kim, Foliations of Minkowski [Formula: see text] spacetime by crooked planes, Int. J. Math. 25(9) (2014) 1450088.].

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Scárdua, Bruno. "Analytic deformations of pencils and integrable one-forms having a first integral." International Journal of Mathematics 31, no. 11 (2020): 2050089. http://dx.doi.org/10.1142/s0129167x20500895.

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We consider integrable analytic deformations of codimension one holomorphic foliations near an initially singular point. Such deformations are of two possible types. The first type is given by an analytic family [Formula: see text] of integrable one-forms [Formula: see text] defined in a neighborhood [Formula: see text] of the initial singular point, and parametrized by the disc [Formula: see text]. The initial foliation is defined by [Formula: see text]. The second type, more restrictive, is given by an integrable holomorphic one-form [Formula: see text] defined in the product [Formula: see t

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Roe, John. "Finite propagation speed and Connes' foliation algebra." Mathematical Proceedings of the Cambridge Philosophical Society 102, no. 3 (1987): 459–66. http://dx.doi.org/10.1017/s0305004100067517.

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In [4], A. Connes has defined the convolution algebra associated to a foliation ℱ of the compact manifold M. Here is the graph or holonomy groupoid of the foliation ℱ (Winkelnkemper [15]). By forming the completion of in its regular representation, he obtains the C*-algebra C*{M, ℱ) associated to the foliation. The completeness of C*(M, ℱ) makes it easier to handle in some analytical contexts, but in others it seems to be too big, and it is necessary to consider instead some carefully selected dense subalgebra (cf. [6]). The purpose of this note is to show that certain spectral functions of le

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Dobrolyubova, Alisa L., and Vladislav E. Kruglov. "Topological conjugacy of non-singular flows with two limit cycles on S2×S1." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 24, no. 1 (2022): 40–53. http://dx.doi.org/10.15507/2079-6900.24.202201.40-53.

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In the paper, non-singular flows with two limit cycles on the manifold S2×S1 are considered. For such flows, a classification is obtained up to topological conjugacy, and it is shown that they have a functional modulus of stability. Since the functional modulus of stability takes on its own value for each fixed argument, the presence of such modulus implies the presence of an infinite number of numerical moduli of stability. To obtain this result, linearization is carried out in the neighbourhoods of two limit cycles using the construction from the work by M. Irwin. A result is obtained on the

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Ndiaye, Ameth, and Aïssa Wade. "Deformations of pairs of codimension one foliations." Advances in Geometry 24, no. 4 (2024): 545–52. http://dx.doi.org/10.1515/advgeom-2024-0023.

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Abstract The notion of a linear deformation of a codimension one foliation into contact structures was introduced in [5]. This concept is a special type of deformation of confoliations. In this paper, we study linear deformations of pairs of codimension one foliations into contact pairs. Applications of our main result are also provided.

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Narmanov, A. Ya, and A. N. Zoyidov. "On the group of diffeomorphisms of foliated manifolds." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 30, no. 1 (2020): 49–58. http://dx.doi.org/10.35634/vm200104.

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Now the foliations theory is intensively developing branch of modern differential geometry, there are numerous researches on the foliation theory. The purpose of our paper is study the structure of the group DiffF(M) of diffeomorphisms and the group IsoF(M) of isometries of foliated manifold (M,F). It is shown the group DiffF(M) is closed subgroup of the group Diff(M) of diffeomorphisms of the manifold M in compact-open topology and also it is proven the group IsoF(M) is Lie group. It is introduced new topology on DiffF(M) which depends on foliation F and called F- compact open topology. It's

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Calvo-Andrade, O., M. Corrêa, and A. Fernández-Pérez. "Higher codimensional foliations with Kupka singularities." International Journal of Mathematics 28, no. 03 (2017): 1750019. http://dx.doi.org/10.1142/s0129167x17500197.

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We consider holomorphic foliations of dimension [Formula: see text] and codimension [Formula: see text] in the projective space [Formula: see text], with a compact connected component of the Kupka set. We prove that if the transversal type is linear with positive integer eigenvalues, then the foliation consists of the fibers of a rational fibration [Formula: see text]. As a corollary, if [Formula: see text] and has a transversal type diagonal with different eigenvalues, then the Kupka component [Formula: see text] is a complete intersection and the leaves of the foliation define a rational fib

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Fukui, Kazuhiko. "Commutators of foliation preserving homeomorphisms for certain compact foliations." Publications of the Research Institute for Mathematical Sciences 34, no. 1 (1998): 65–73. http://dx.doi.org/10.2977/prims/1195144828.

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Boyom, Michel Nguiffo. "Linear Gauge and the Linearization Problem for Webs." Journal of the Tensor Society 8, no. 01 (2007): 1–16. http://dx.doi.org/10.56424/jts.v8i01.10562.

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Regarding the theory of foliation, some aspects of the theory of Riemannian foliations have been brought in completion by the Molino theory. Such a structure is defined by some finite dimensional Lie subalgebra of the Lie algebra of transverse vector fields. The problem I am interested in is more modeste. It is to get sufficient conditions for a smooth manifold admitting foliations with transverse (pseudo) Riemannian metrics. The investigation is inspired by both methods of information geometry and the Hessian geometry.

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March, Peter, Maung Min-Oo, and Ernst A. Ruh. "Mean Curvature of Riemannian Foliations." Canadian Mathematical Bulletin 39, no. 1 (1996): 95–105. http://dx.doi.org/10.4153/cmb-1996-012-4.

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AbstractIt is shown that a suitable conformai change of the metric in the leaf direction of a transversally oriented Riemannian foliation on a closed manifold will make the basic component of the mean curvature harmonic. As a corollary, we deduce vanishing and finiteness theorems for Riemannian foliations without assuming the harmonicity of the basic mean curvature.

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42

Wilson, Matthew Coffie, Chiri G. Amedjoe, and Simon K. Y. Gawu. "STRUCTURES OF BIRIMIAN AND TARKWAIAN ROCKS AT NORTH-WEST NEW DROBO – IMPLICATION ON DEFORMATION." Malaysian Journal of Geosciences 6, no. 1 (2022): 36–44. http://dx.doi.org/10.26480/mjg.01.2022.36.44.

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This research leads to identifying the microstructures, the deformation episodes (D) and foliation grades (S) of rocks in the study area. Different geological structures such as shear zones, foliations, micro-faults, crack-seal events, etc. have been identified in the study area. Different phases of deformation episodes and foliation grades have been studied to determine the deformation environments. Senses of shear such as dextral, CS, and CS’ as well as antithetic and synthetic micro-faults and boudins may be identified at the north-west New Drobo. Three (3) main deformational (D) events and

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Baird, Paul, and Jean-Marie Burel. "Conformal subfoliations of prescribed geodesic curvature." MATHEMATICA SCANDINAVICA 93, no. 2 (2003): 221. http://dx.doi.org/10.7146/math.scand.a-14420.

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Given a $2$-dimensional conformal foliation $\mathcal F$ of a Riemannian manifold $M$, the problem of finding a $1$-dimensional subfoliation $\mathcal G$, conformal in $M$, whose leaves have prescribed geodesic curvature in the leaves of $\mathcal F$ is equivalent to a Pfaff differential system on a circle bundle over $M$. We study such pairs of foliations on a $3$- and $4$-manifold.

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GELBUKH, IRINA. "ON COLLINEAR CLOSED ONE-FORMS." Bulletin of the Australian Mathematical Society 84, no. 2 (2011): 322–36. http://dx.doi.org/10.1017/s0004972711002310.

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AbstractWe study one-forms with zero wedge-product, which we call collinear, and their foliations. We characterise the set of forms that define a given foliation, with special attention to closed forms and forms with small singular sets. We apply the notion of collinearity to give a criterion for the existence of a compact leaf and to study homological properties of compact leaves.

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BONATTI, CHRISTIAN, XAVIER GÓMEZ-MONT, and MATILDE MARTÍNEZ. "Foliated hyperbolicity and foliations with hyperbolic leaves." Ergodic Theory and Dynamical Systems 40, no. 4 (2018): 881–903. http://dx.doi.org/10.1017/etds.2018.61.

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Given a lamination in a compact space and a laminated vector field $X$ which is hyperbolic when restricted to the leaves of the lamination, we distinguish a class of $X$-invariant probabilities that describe the behavior of almost every $X$-orbit in every leaf, which we call Gibbs $u$-states. We apply this to the case of foliations in compact manifolds having leaves with negative curvature, using the foliated hyperbolic vector field on the unit tangent bundle to the foliation generating the leaf geodesics. When the Lyapunov exponents of such ergodic Gibbs $u$-states are negative, it is an SRB

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ALCÁNTARA, CLAUDIA R. "GEOMETRIC INVARIANT THEORY FOR HOLOMORPHIC FOLIATIONS ON ℂℙ2 OF DEGREE 2". Glasgow Mathematical Journal 53, № 1 (2010): 153–68. http://dx.doi.org/10.1017/s0017089510000674.

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AbstractLet 2 be the space of the holomorphic foliations on ℂℙ2 of degree 2. In this paper we study the linear action PGL(3, ℂ) × 2 → 2 given by gX = DgX ^(g−1) in the sense of the Geometric Invariant Theory. We obtain a characterisation of unstable and stable foliations according to properties of singular points and existence of invariant lines. We also prove that if X is an unstable foliation of degree 2, then X is transversal with respect to a rational fibration. Finally we prove that the geometric quotient of non-degenerate foliations without invariant lines is the moduli space of polarise

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BONATTI, CH, X. GÓMEZ-MONT, and R. VILA-FREYER. "Statistical behaviour of the leaves of Riccati foliations." Ergodic Theory and Dynamical Systems 30, no. 1 (2009): 67–96. http://dx.doi.org/10.1017/s0143385708001028.

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AbstractWe introduce the geodesic flow on the leaves of a holomorphic foliation with leaves of dimension one and hyperbolic, corresponding to the unique complete metric of curvature −1 compatible with its conformal structure. We do these for the foliations associated to Riccati equations, which are the projectivization of the solutions of linear ordinary differential equations over a finite Riemann surface of hyperbolic type S, and may be described by a representation ρ:π1(S)→GL(n,ℂ). We give conditions under which the foliated geodesic flow has a generic repeller–attractor statistical dynamic

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Zhang, Ji’en, Hongrui Fan, Wenjiao Xiao, et al. "Configuration of Carbonatite Constrained in Preintrusion Transpositional Foliation in the Bayan Obo Giant Rare Earth Element Deposit, China." Economic Geology 119, no. 4 (2024): 853–69. http://dx.doi.org/10.5382/econgeo.5076.

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Abstract The Bayan Obo ore deposit is the largest rare earth element (REE) deposit in the world and has been assumed to be hosted in dolomite that was folded in a syncline. This has been challenged by results from drill holes and low-resistivity, controlled-source audio-frequency magnetotellurics (CSAMT) survey. In this paper, we present structural analysis of clastic sedimentary rocks from around the deposit, their relationship with carbonatite, and the orientations of the carbonatite bodies and dikes to constrain the possible configuration of carbonatite. Clastic sedimentary rocks underwent

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Androulidakis, Iakovos, and Marco Zambon. "Stefan–Sussmann singular foliations, singular subalgebroids and their associated sheaves." International Journal of Geometric Methods in Modern Physics 13, Supp. 1 (2016): 1641001. http://dx.doi.org/10.1142/s0219887816410012.

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We explain and motivate Stefan–Sussmann singular foliations, and by replacing the tangent bundle of a manifold with an arbitrary Lie algebroid, we introduce singular subalgebroids. Both notions are defined using compactly supported sections. The main results of this note are an equivalent characterization, in which the compact support condition is removed, and an explicit description of the sheaf associated to any Stefan–Sussmann singular foliation or singular subalgebroid.

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Arslan, Arzu, Cees W. Passchier, and Daniel Koehn. "Foliation boudinage." Journal of Structural Geology 30, no. 3 (2008): 291–309. http://dx.doi.org/10.1016/j.jsg.2007.11.004.

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