Relevant bibliographies by topics / Flat submanifold

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Flat submanifold'

Author: Grafiati
Published: 28 May 2022
Last updated: 31 July 2025

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Journal articles on the topic "Flat submanifold"

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Blair, David E. "On Lagrangian Catenoids." Canadian Mathematical Bulletin 50, no. 3 (2007): 321–33. http://dx.doi.org/10.4153/cmb-2007-031-4.

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AbstractRecently I. Castro and F.Urbano introduced the Lagrangian catenoid. Topologically, it is ℝ × Sn–1 and its induced metric is conformally flat, but not cylindrical. Their result is that if a Lagrangian minimal submanifold in ℂn is foliated by round (n – 1)-spheres, it is congruent to a Lagrangian catenoid. Here we study the question of conformally flat, minimal, Lagrangian submanifolds in ℂn. The general problem is formidable, but we first show that such a submanifold resembles a Lagrangian catenoid in that its Schouten tensor has an eigenvalue of multiplicity one. Then, restricting to t
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Kumar, Sangeet, Rakesh Kumar, and R. K. Nagaich. "Characterization of Holomorphic Bisectional Curvature ofGCR-Lightlike Submanifolds." Advances in Mathematical Physics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/356263.

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We obtain the expressions for sectional curvature, holomorphic sectional curvature, and holomorphic bisectional curvature of aGCR-lightlike submanifold of an indefinite Kaehler manifold. We discuss the boundedness of holomorphic sectional curvature ofGCR-lightlike submanifolds of an indefinite complex space form. We establish a condition for aGCR-lightlike submanifold of an indefinite complex space form to be null holomorphically flat. We also obtain some characterization theorems for holomorphic sectional and holomorphic bisectional curvature.
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Ali A. Shihab and Mihail Banaru. "ON SPECTRA OF SOME TENSORS OF SIX-DIMENSINAL KÄHLERIAN AND NEARLY-KÄHLERIAN SUBMANIFOLDS OF CAYLEY ALGEBRA." Tikrit Journal of Pure Science 20, no. 4 (2023): 42–147. http://dx.doi.org/10.25130/tjps.v20i4.1227.

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Six-dimensional Kählerian and nearly-Kählerian submanifolds of Cayley algebra are considered. Spectra of some classical tensors of such submanifolds of the octave algebra are computed. It is proved that a nearly-Kählerian six-dimensional submanifold of Cayley algebra is conharmonically flat if and only if it is holomorphically isometric to the complex Euclidean space with a canonical Kählerian structure.
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Bashir, M. A. "On Totally Real Submanifolds in a 6-Sphere." Canadian Mathematical Bulletin 33, no. 2 (1990): 162–66. http://dx.doi.org/10.4153/cmb-1990-027-4.

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AbstractThe 6-dimensional sphere S6 has an almost complex structure induced by properties of Cayley algebra. With respect to this structure S6 is a nearly Kaehlerian manifold. We investigate 2-dimensional totally real submanifolds in S6. We prove that a 2-dimensional totally real submanifold in S6 is flat.
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Kim, Jihun, Jeonghyeong Park, and Bayram Şahin. "Weakly Einstein Equivalence in a Golden Space Form and Certain CR-submanifolds." Mathematica Slovaca 73, no. 6 (2023): 1615–27. http://dx.doi.org/10.1515/ms-2023-0117.

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ABSTRACT It is known that the Golden space form may not be an Einstein manifold. In this paper, it is shown that the condition to be Einstein for a Golden space form is equivalent to being weakly Einstein. In addition, the partial geodesic and cyclic parallelism of the CR-submanifolds of a Golden space are examined, and the case of the constant Golden sectional curvature is determined. Moreover, the CR-submanifolds with semi-flat normal connection are studied and an inequality is obtained. The equality case of this inequality is also checked. We also consider the totally umbilical CR-submanifo
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Aquib, Mohd, Michel Nguiffo Boyom, Mohammad Hasan Shahid, and Gabriel-Eduard Vîlcu. "The First Fundamental Equation and Generalized Wintgen-Type Inequalities for Submanifolds in Generalized Space Forms." Mathematics 7, no. 12 (2019): 1151. http://dx.doi.org/10.3390/math7121151.

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In this work, we first derive a generalized Wintgen type inequality for a Lagrangian submanifold in a generalized complex space form. Further, we extend this inequality to the case of bi-slant submanifolds in generalized complex and generalized Sasakian space forms and derive some applications in various slant cases. Finally, we obtain obstructions to the existence of non-flat generalized complex space forms and non-flat generalized Sasakian space forms in terms of dimension of the vector space of solutions to the first fundamental equation on such spaces.
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Upreti, Jaya, and Shankar Lal. "On H-Projectively flat KH-Structure submanifold." Journal of the Tensor Society 1, no. 01 (2007): 41–49. http://dx.doi.org/10.56424/jts.v1i01.9947.

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In this paper we have obtained the condition for a submanifold of a KH-structure manifold to be KH-structure. A few relations are found in the second fundamental tensor H and k. Using these results we have also find out the flatness of H-projective curvature tensor in KH-structure submanifold.
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Shugailo, Olena. "On curve based ruled affine submanifolds." Proceedings of the International Geometry Center 17, no. 3 (2024): 203–17. https://doi.org/10.15673/pigc.v17i3.2883.

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In this paper we consider affine ruled submanifolds of arbitrary dimension and codimension in the classical sense, i.e. curve based ones. For such a submanifold we define the natural parameterization and the natural transversal distribution. We calculate all the affine characteristics for such an affine immersion. We find conditions on the base curve and the directions of the rectilinear generators such that the induced connection is flat and the natural transversal distribution is equiaffine.
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Ghazal, Tahsin, and Sharief Deshmukh. "Submanifolds of Euclidean space with parallel mean curvature vector." International Journal of Mathematics and Mathematical Sciences 14, no. 3 (1991): 533–36. http://dx.doi.org/10.1155/s0161171291000728.

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The object of the paper is to study some compact submanifolds in the Euclidean spaceRnwhose mean curvature vector is parallel in the normal bundle. First we prove that there does not exist ann-dimensional compact simply connected totally real submanifold inR2nwhose mean curvature vector is parallel. Then we show that then-dimensional compact totally real submanifolds of constant curvature and parallel mean curvature inR2nare flat. Finally we show that compact Positively curved submanifolds inRnwith parallel mean curvature vector are homology spheres. The last result in particular for even dime
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Mihai, Ion, and Yoshihiko Tazawa. "On 3-dimensional contact slant submanifolds in Sasakian space forms." Bulletin of the Australian Mathematical Society 68, no. 2 (2003): 275–83. http://dx.doi.org/10.1017/s0004972700037655.

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Recently, B.-Y. Chen obtained an inequality for slant surfaces in complex space forms. Further, B.-Y. Chen and one of the present authors proved the non-minimality of proper slant surfaces in non-flat complex space forms. In the present paper, we investigate 3-dimensional proper contact slant submanifolds in Sasakian space forms. A sharp inequality is obtained between the scalar curvature (intrinsic invariant) and the main extrinsic invariant, namely the squared mean curvature.It is also shown that a 3-dimensional contact slant submanifold M of a Sasakian space form M̆(c), with c ≠ 1, cannot b
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Dissertations / Theses on the topic "Flat submanifold"

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Борисенко, Олексій Андрійович, Алексей Андреевич Борисенко, Oleksii Andriiovych Borysenko та Е. В. Татарко. "О строении трехмерных поверхностей с метрикой вращения". Thesis, Сумский государственный университет, 2014. http://essuir.sumdu.edu.ua/handle/123456789/39365.

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Многомерная риманова метрика называется метрикой вращения. При этом поверхность, несущая метрику вращения, не обязательно является поверхностью вращения. Тогда возникает вопрос о том, какие условия нужны для того, чтобы подмногообразия с метрикой вращения были многомерными поверхностями вращения.
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ROSSI, FEDERICO ALBERTO. "D-Complex Structures on Manifolds: Cohomological properties and deformations." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2013. http://hdl.handle.net/10281/41976.

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In questa tesi studiamo alcune proprietà delle "Varietà Doppie" o D-Varietà. In particolare studiamo la teoria delle deformazioni di D-Strutture e di D-Strutture CR, e troviamo una condizione che è equivalente alla classica condizione di Maurer-Cartan che descrive l'integrabilità di deformazioni di D-Strutture. Successivamente prestiamo attenzione alla coomologia delle D-Varietà, provando che una versione D-complessa del del-delbar-Lemma non può essere vera per D-varietà compatte. Inoltre sono stabilite alcune proprietà di sottogruppi speciali della coomologia di de-Rham, ottenute studiando il
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Brander, David. "Flat submanifolds of a sphere and integrable systems." Phd thesis, 2005. http://hdl.handle.net/1885/150843.

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Book chapters on the topic "Flat submanifold"

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Dajczer, Marcos, and Ruy Tojeiro. "Conformally Flat Submanifolds." In Universitext. Springer US, 2019. http://dx.doi.org/10.1007/978-1-4939-9644-5_16.

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de Dios Pérez, Juan. "Derivatives on Real Hypersurfaces of Non-flat Complex Space Forms." In Hermitian–Grassmannian Submanifolds. Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-5556-0_3.

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Conference papers on the topic "Flat submanifold"

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Defever, Filip, and Udo Hertrich-Jeromin. "Three-dimensional conformally flat hypersurfaces." In Geometry and Topology of Submanifolds IX. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812817976_0011.

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Martínez, Antonio, and Francisco Milán. "Some results on projectively flat affine surfaces." In PDEs, Submanifolds and Affine Differential Geometry. Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc69-0-11.

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Leder, Judith. "Cubic forms generated by functions on projectively flat spaces." In Geometry and Topology of Submanifolds IX. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812817976_0017.

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Deszcz, Ryszard, Leopold Verstraelen, and Şahnur Yaprak. "HYPERSURFACES WITH PSEUDOSYMMETRIC WEYL TENSOR IN CONFORMALLY FLAT MANIFOLDS." In Geometry and Topology of Submanifolds IX. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812817976_0012.

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You might also be interested in the extended bibliographies on the topic 'Flat submanifold' for particular source types:
Journal articles
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