Results 81 to 90 of about 17,898 (118)

TOTALLY η-UMBILIC HYPERSURFACES IN A NONFLAT COMPLEX SPACE FORM AND THEIR ALMOST CONTACT METRIC STRUCTURES

Scientiae Mathematicae Japonicae, 2010
KIM, BYUNG HAK, MAEDA, SADAHIRO
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A characterization of totally umbilical hypersurfaces in de Sitter space

Journal of Geometry and Physics, 2004
Let \(M^n\) be a compact space-like hypersurface in de Sitter space and let \(H_k\) denotes \(k\)-th mean curvature function of \(M^n\). The authors prove that if \(M^n\) is contained in the chronological future (or past) of an equator of de Sitter space then \(M^n\) is a totally umbilical round sphere if there exist nonnegative constants \(C_1,C_2 ...
Koh, Sung-Eun, Yoo, Myung-Suk
exaly   +4 more sources

Non-immersibility of a space form as a totally umbilical hypersurface

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1988
SynopsisSuppose that a space form is immersed into another Riemannian manifold as a totally umbilical hypersurface with constant mean curvature. Then, in the ambient manifold, the lengthof the curvature tensor, that of the Ricci tensor and the scalar curvature must satisfy an inequality. In this paper the authors proved the inequality.
Okumura, Masafumi, Takahashi, Hiroshi
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Rigidity for Closed Totally Umbilical Hypersurfaces in Space Forms

Journal of Geometric Analysis, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xu Cheng, Detang Zhou, Zhou Detang
exaly   +3 more sources

Geometry of hypersurface $$\gamma \times H^2$$ γ × H 2 in the geometry of Thurston $$F^{4}$$ F 4

Beitrage Zur Algebra Und Geometrie, 2018
M. Belkhelfa, Halima Boukhari, Abdelbasset Hasni̇   +2 more
exaly   +2 more sources

TOTALLY UMBILIC HYPERSURFACES AND ISOPARAMETRIC HYPERSURFACES IN SPACE FORMS

Contemporary Aspects of Complex Analysis, Differential Geometry and Mathematical Physics, 2005
In differential geometry it is interesting to know the shape of a Riemannian submanifold by the extrinsic shape of geodesics and circles of positive curvature of the submanifold in an ambient Riemannian manifold. For example, it is known that a hypersurface M n in a Euclidean space Wn+' is locally a standard sphere if and only if every geodesic of M is
MAKOTO KIMURA, SADAHIRO MAEDA
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Quantitative Stability for Anisotropic Nearly Umbilical Hypersurfaces

Journal of Geometric Analysis, 2017
We prove qualitative and quantitative stability of the following rigidity theorem: the only anisotropic totally umbilical closed hypersurface is the Wulff shape. Consider $$n \ge 2$$n≥2, $$p\in (1, \, +\infty )$$p∈(1,+∞) and $$\Sigma $$Σ an n-dimensional,
A. De Rosa, Stefano Gioffrè
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Legendre magnetic flows for totally η-umbilic real hypersurfaces in a complex hyperbolic space

Differential Geometry and its Applications, 2023
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Shi, Qingsong, Adachi, Toshiaki
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A constrained mean curvature flow on capillary hypersurface supported on totally geodesic plane

Communications in Contemporary Mathematics
We prove a new Minkowski type formula for capillary hypersurfaces supported on totally geodesic hyperplanes in hyperbolic space. It leads to a volume-preserving flow starting from a star-shaped initial hypersurface.
Xiaoxiang Chai, Yiming Chen
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Codimension-two spacelike submanifolds with umbilical lightlike normal sections and their relationship to lightlike hypersurfaces

Classical and quantum gravity
We study codimension-two spacelike submanifolds in Lorentzian spacetimes that admit umbilical lightlike normal directions. We show that such submanifolds are subject to strong geometric and topological constraints, establishing explicit relationships ...
J. Gómez
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