Results 101 to 110 of about 179 (133)

On Riemannian spaces admitting a family of totally umbilical hypersurfaces, I

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1951
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On the Morse index of free-boundary CMC hypersurfaces in the upper hemisphere

We prove results for free-boundary hypersurfaces in the upper unit hemisphere $\mathbb{S}^{n+1}_{+}$ of $\mathbb{R}^{n+2}$. First we show that if the norm squared of the second fundamental form is constant, the Morse index of a free-boundary minimal ...
de Oliveira, Crísia Ramos
core  

Parallel and totally umbilical hypersurfaces of the four-dimensional Thurston geometry Sol₀⁴

sponsorship: M. D'haene is supported by Methusalem grant METH/21/03-long-term structural funding of the Flemish Government. J. Inoguchi is partially supported by JSPS KAKENHI Grant Numbers 23K03081 and 19K03461. J. Van der Veken is supported by the Research Foundation-Flanders (FWO) and the National Natural Science Foundation of China (NSFC) under ...
D'haene, Marie, Inoguchi, Jun-ichi, Van der Veken, Joeri   +2 more
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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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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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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 ...
Sung-Eun Koh
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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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