Results 11 to 20 of about 8,022 (261)
A Classification of a Totally Umbilical Slant Submanifold of Cosymplectic Manifolds [PDF]
Abstract and Applied Analysis, 2012 We study slant submanifolds of a cosymplectic manifold. It is shown that a totally umbilical slant submanifold 𝑀 of a cosymplectic manifold 𝑀 is either an anti-invariant submanifold or a 1−dimensional submanifold.
Siraj Uddin, Cenap Ozel, Viqar Azam Khan
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Totally Umbilical Hemi-Slant Submanifolds of Kaehler Manifolds [PDF]
Abstract and Applied Analysis, 2011 We study totally umbilical hemi-slant submanifolds of a Kaehler manifold via curvature tensor. We prove some classification theorems for totally umbilical hemi-slant submanifolds of a Kaehler manifold and give an example.
Falleh R. Al-Solamy +2 more
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On totally umbilical CR-submanifolds of a Kaehler manifold [PDF]
International Journal of Mathematics and Mathematical Sciences, 1993 Let M be a compact 3-dimensional totally umbilical CR-submanifold of a Kaehler manifold of positive holomorphic sectional curvature. We prove that if the length of the mean curvature vector of M does not vanish, then M is either diffeomorphic to S3 or ...
M. A. Bashir
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Totally umbilical hypersurfaces of product spaces [PDF]
manuscripta mathematica, 2021 Given a Riemannian manifold $M,$ and an open interval $I\subset\mathbb{R},$ we characterize nontrivial totally umbilical hypersurfaces of the product $M\times I$ -- as well as of warped products $I\times_ωM$ -- as those which are local graphs built on isoparametric families of totally umbilical hypersurfaces of $M.$ By means of this characterization ...
Ronaldo F. de Lima +1 more
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Planar Pseudo-geodesics and Totally Umbilic Submanifolds [PDF]
The Journal of Geometric Analysis, 2023 AbstractWe study totally umbilic isometric immersions between Riemannian manifolds. First, we provide a novel characterization of the totally umbilic isometric immersions with parallel normalized mean curvature vector, i.e., those having nonzero mean curvature vector and such that the unit vector in the direction of the mean curvature vector is ...
Steen Markvorsen, Matteo Raffaelli
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Characterization of totally umbilical hypersurfaces [PDF]
Proceedings of the American Mathematical Society, 1981 This paper gives a sufficient condition for a complete hypersurface of a Riemannian manifold of constant curvature to be umbilical. The condition will be given by an inequality which is established between the length of the second fundamental tensor and the mean curvature. K. Nomizu and B.
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Hiroshima Mathematical Journal, 1990 Let M be a complete hypersurface with constant mean curvature of a space form of index s \((=0\) or 1). A sufficient condition, which is established between the length of the second fundamental form and the mean curvature, is given for M to be totally umbilical. This result generalizes the reviewer's result [Proc. Am. Math. Soc.
Cheng, Qing Ming, Nakagawa, Hisao
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CONFORMAL VECTOR FIELDS AND TOTALLY UMBILIC HYPERSURFACES [PDF]
Bulletin of the Korean Mathematical Society, 2002 Let \((M^n,g)\), \(n\geq 2\), be a connected semi-Riemannian hypersurface of a semi-Riemannian space form \((\overline{M}_k^{n+1}(\overline{c}),\overline{g})\) of signature \(k\). Assume that the ambient manifold carries a conformal vector field \(V\) such that the tangential part \((V|M^n)^T\) becomes a conformal vector field on the hypersurface. Then
Kim, Dong-Soo +3 more
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Totally umbilical lightlike submanifolds
Kodai Mathematical Journal, 2003 In the paper under review the authors study the geometry of totally umbilical light-like submanifolds. First they recall some results for light-like submanifolds and their structure equations. Next they prove several new theorems on such submanifolds in semi-Riemannian manifolds of constant curvature.
Duggal, K. L., Jin, D. H.
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GMS Interdisciplinary Plastic and Reconstructive Surgery DGPW, 2021 Background: Abdominal wall hernias are frequent in patients with peritoneal dialysis. Guidelines recommend an open hernia repair with extraperitoneal mesh placement to avoid access to the abdominal cavity.
Bauer, Katrin +4 more
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