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Totally umbilical submanifolds in some semi-Riemannian manifolds [PDF]
Colloquium Mathematicum, 2010 openaire +1 more source
TOTALLY UMBILICAL CR-SUBMANIFOLDS OF KÄHLER MANIFOLDS
TOTALLY UMBILICAL CR-SUBMANIFOLDS OF KÄHLER MANIFOLDSopenaire
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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Submanifolds with totally umbilical Gauss image
Geometriae Dedicata, 1996The 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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Totally umbilical CR-submanifolds of nearly K�hler manifolds
Geometriae Dedicata, 1994A classification theorem for totally umbilical CR-submanifolds of nearly- Kähler manifolds is obtained. The statement and the proof are similar to the corresponding ones in a Kählerian ambient.
Khan, K. A., Khan, V. A., Husain, S. I.
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Totally contact-umbilical semi-invariant submanifolds of a Sasakian manifold
SUT Journal of Mathematics, 2002The main result of this paper is that a proper, non-totally contact-geodesic, totally contact-umbilical semi-invariant \(m\)-dimensional (\(m>4\)) submanifold of a Sasakian manifold, must be a generalized Hopf manifold. Let \(M\) be an \(m\)-dimensional submanifold of a \((2n+1)\)-dimensional Sasakian manifold \((N,\phi,\xi,\eta,g)\).
Kon, S.H., Loo, Tee-How
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On pinching theorems for compact pseudo-umbilical submanifold
Demonstratio Mathematica, 2012 Consider submanifolds in the nested space. For a compact pseudoumbilical submanifold with parallel mean curvature vector of a Riemannian submanifold with constant curvature immersed in a quasi-constant curvature Riemannian manifold, two sufficient ...
Jing Mao
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Totally umbilical hemislant submanifolds of LP-Sasakian manifold
Lobachevskii Journal of Mathematics, 2015Arindam Bhattacharyya +2 more
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Totally umbilical submanifolds of Kaehler manifolds
Archiv der Mathematik, 1981Bang‐Yen Chen
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Conformal Killing Forms on Totally Umbilical Submanifolds
Journal of Mathematical Sciences, 2016For 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. +3 more
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