Results 111 to 120 of about 207 (126)
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Family of Totally Umbilical Hypersurfaces in an Einstein Space
Annals of Mathematics, 1943Yung-Chow Wong
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Totally umbilical degenerate Monge hypersurfaces of R 2 4
1996The purpose of the paper is to determine all totally umbilical degenerate Monge hypersurfaces of R 4 2 . To this end, we recall the terminology and few results from Bejancu - Duggal [1].
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Current Developments in Differential Geometry and its Related Fields, 2015
Galia Nakova
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Galia Nakova
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TOTALLY UMBILIC HYPERSURFACES AND ISOPARAMETRIC HYPERSURFACES IN SPACE FORMS
Contemporary Aspects of Complex Analysis, Differential Geometry and Mathematical Physics, 2005In 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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Rigidity for Closed Totally Umbilical Hypersurfaces in Space Forms
The Journal of Geometric Analysis, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cheng, Xu, Zhou, Detang
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Legendre magnetic flows for totally η-umbilic real hypersurfaces in a complex hyperbolic space
Differential Geometry and its Applications, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shi, Qingsong, Adachi, Toshiaki
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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, 1988SynopsisSuppose 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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Codazzi and totally umbilical hypersurfaces in $\mathrm {Sol}_1^4$
Glasgow Mathematical JournalAbstractIn this paper, we prove the non-existence of Codazzi and totally umbilical hypersurfaces, especially totally geodesic hypersurfaces, in the $4$ -dimensional model space $\mathrm {Sol}_1^4$ .
Zlatko Erjavec, Jun-ichi Inoguchi
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ON RIEMANNIAN MANIFOLDS WHICH ADMIT A PARALLEL FAMILY OF TOTALLY UMBILICAL HYPERSURFACES
The Quarterly Journal of Mathematics, 1985A parallel family of totally umbilical hypersurfaces in a Riemannian manifold is a smooth 1-parameter family of codimension -1 totally umbilical submanifolds every two of which are locally a constant distance apart. A perfect example is a family of concentric spheres in Euclidean space or some other space form.
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2020
Some relations involving the Ricci and scalar curvatures of totally $\eta$-umbilical real hypersurfaces of a complex space form are examined. With the help of these relations, some results on totally $\eta$-umbilical real hypersurfaces of a complex space form are given.
DENİZ, Özlem, GÜLBAHAR, Mehmet
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Some relations involving the Ricci and scalar curvatures of totally $\eta$-umbilical real hypersurfaces of a complex space form are examined. With the help of these relations, some results on totally $\eta$-umbilical real hypersurfaces of a complex space form are given.
DENİZ, Özlem, GÜLBAHAR, Mehmet
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