Results 111 to 120 of about 1,215 (136)

Totally Umbilical Submanifolds in Sasakian Manifolds

Totally Umbilical Submanifolds in Sasakian Manifolds
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Totally Contact Umbilical Submanifolds in Sasakian Manifolds

Totally Contact Umbilical Submanifolds in Sasakian Manifolds
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Totally umbilical submanifolds in normal contact Riemannian Manifolds

Totally umbilical submanifolds in normal contact Riemannian Manifolds
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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.
K L Duggal
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A classification of totally geodesic and totally umbilical Legendrian submanifolds of $$(\kappa ,\mu )$$ ( κ , μ ) -spaces [PDF]

Annals of Global Analysis and Geometry, 2018
We present classifications of totally geodesic and totally umbilical Legendrian submanifolds of $(κ,μ)$-spaces with Boeckx invariant $I \leq -1$. In particular, we prove that such submanifolds must be, up to local isometries, among the examples that we explicitly construct.
Alfonso Carriazo, Veronica Martín-Molina, Luc Vrancken   +2 more
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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 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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On a class of submanifolds carrying an extrinsic totally umbilical foliation

Israel Journal of Mathematics, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dajczer, M., Florit, L. A., Tojeiro, R.
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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.
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