Results 81 to 90 of about 126 (113)

Totally umbilical submanifolds in normal contact Riemannian Manifolds

Hokkaido Mathematical Journal, 1972
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TOTALLY UMBILICAL CR-SUBMANIFOLDS OF KÄHLER MANIFOLDS

TOTALLY UMBILICAL CR-SUBMANIFOLDS OF KÄHLER MANIFOLDS
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ON TOTALLY UMBILICAL SUBMANIFOLDS OF SOME CLASS RIEMANNIAN MANIFOLDS

Demonstratio Mathematica, 1983
The authors study totally umbilical submanifolds M with parallel mean curvature vector in pseudo-Riemannian manifolds N, such that the curvature tensor R of M satisfies \(R(X,Y)\cdot R=0\), while N carries a generalized curvature tensor \(\tilde T\) with \(\tilde R\)(X,Y)\(\cdot \tilde T=0\), \(\tilde R\) being the curvature of N.
Ryszard Deszcz
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ON TOTALLY UMBILICAL SUBMANIFOLDS OF CARTAN-SYMMETRIC MANIFOLDS

Demonstratio Mathematica, 1976
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Totally umbilical submanifolds inG(2,n). II

Journal of Mathematical Sciences, 1994
A submanifold \(N\) in a Riemannian manifold \(M\) is called totally umbilical if its second fundamental form is proportional to the first fundamental form. In this note, the author continues the study of totally umbilical submanifolds in symmetric spaces. In [the author, Mat. Fiz. Anal. Geom.
Yu A Nikolaevskii
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Conformal Killing Forms on Totally Umbilical Submanifolds

Journal of Mathematical Sciences, 2016
For a \(C^{\infty}\)-manifold \(M\) with a pseudo-Riemannian metric \(g\) and Levi-Civita connection \(\nabla\), an \(r\)-form \(\omega\) on \(M\) is called a conformal Killing form if it satisfies the differential equation: \[ \nabla\omega-\frac{1}{r+1}d\omega+g\wedge\theta=0 \] for some \((r-1)\)-form \(\theta\).
Stepanov, S. E., Alexandrova, I. A., Tsyganok, I. I., Mikeš, Josef   +3 more
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Submanifolds with totally umbilical Gauss image

Geometriae Dedicata, 1996
The submanifolds whose Gauss images are totally umbilical submanifolds of a Grassmannian manifold are considered. The main result is the following classification theorem: if the Gauss image of a submanifold \(F\) in a Euclidean space is totally umbilical, then either the Gauss image is totally geodesic, or \(F\) is a surface in \(E^n\) of special ...
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On totally umbilical submanifolds of Finsler spaces

Annales Polonici Mathematici, 2011
The authors define totally umbilical submanifolds of Finsler manifolds using the second fundamental form introduced by Q. He and Y. B. Shen. They study totally umbilical submanifolds of Finsler manifolds establishing some simpler equations related to curvatures of Finsler submanifolds and the curvatures of the ambient space.
He, Qun, Yang, Wei, Zhao, Wei
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Totally umbilical CR-submanifolds of Kähler manifolds

TRU Mathematics, 1985
The authors prove the following important result. Any connected non totally geodesic but totally umbilical proper CR-submanifold of dimension greater than 4 in a Kähler manifold is a Sasakian manifold.
TOYONARI, TOSHITAKA, NEMOTO, HIROAKI
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On totally umbilical submanifolds ofS n+p

Israel Journal of Mathematics, 2000
Let \(M\) be an \(n\)-dimensional compact minimal submanifold in \(S^{n+p}\). \textit{A. M. Li} and \textit{J. M. Li} proved a scalar curvature pinching theorem [Arch. Math. 58, 582-594 (1992; Zbl 0767.53042)]. \textit{S.-T. Yau} proved a sectional curvature pinching theorem [Am. J. Math. 97, 76-100 (1975; Zbl 0304.53042)]. \textit{N.
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