Totally umbilical submanifolds inG(2,n). II

1994 ◽  
Vol 72 (4) ◽  
pp. 3212-3222
Author(s):  
Yu. A. Nikolaevskii
Keyword(s):  
Totally Umbilical ◽  
Totally Umbilical Submanifolds

Conformal Killing Forms on Totally Umbilical Submanifolds

2016 ◽  
Vol 217 (5) ◽  
pp. 525-539 ◽  
Author(s):  
S. E. Stepanov ◽  
I. A. Alexandrova ◽  
I. I. Tsyganok ◽  
J. Mikeš
Keyword(s):  
Conformal Killing ◽  
Totally Umbilical ◽  
Totally Umbilical Submanifolds

scholarly journals Totally umbilical submanifolds of quaternion-space-forms

1978 ◽  
Vol 26 (2) ◽  
pp. 154-162 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Space Forms ◽  
Totally Umbilical ◽  
Quaternion Space ◽  
Totally Umbilical Submanifolds

AbstractTotally umbilical submanifolds of dimension greater than four in quaternion-space-forms are completely classified.

scholarly journals On the umbilicity of linear Weingarten spacelike submanifolds immersed in the de Sitter space

2020 ◽  
pp. 1-12
Author(s):  
Weiller F. C. Barboza ◽  
Eudes L. de Lima ◽  
Henrique F. de Lima ◽  
Marco Antonio L. Velásquez
Keyword(s):  
Mean Curvature ◽  
Curvature Vector ◽  
De Sitter Space ◽  
Index Formula ◽  
Curvature Function ◽  
De Sitter ◽  
Totally Umbilical ◽  
Spacelike Submanifold ◽  
Totally Umbilical Submanifolds ◽  
Spacelike Submanifolds

We investigate the umbilicity of [Formula: see text]-dimensional complete linear Weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector field in the de Sitter space [Formula: see text] of index [Formula: see text]. We recall that a spacelike submanifold is said to be linear Weingarten when its mean curvature function [Formula: see text] and its normalized scalar curvature [Formula: see text] satisfy a linear relation of the type [Formula: see text], for some constants [Formula: see text]. Under suitable constraints on the values of [Formula: see text] and [Formula: see text], we apply a generalized maximum principle for a modified Cheng–Yau operator [Formula: see text] in order to show that such a spacelike submanifold must be either totally umbilical or isometric to a product [Formula: see text], where the factors [Formula: see text] are totally umbilical submanifolds of [Formula: see text] which are mutually perpendicular along their intersections. Moreover, we also study the case in which these spacelike submanifolds are [Formula: see text]-parabolic.

On totally umbilical submanifolds of Finsler spaces

2011 ◽  
Vol 100 (2) ◽  
pp. 147-157
Author(s):  
Qun He ◽  
Wei Yang ◽  
Wei Zhao
Keyword(s):  
Finsler Spaces ◽  
Totally Umbilical ◽  
Totally Umbilical Submanifolds

scholarly journals Totally umbilical submanifolds in irreducible symmetric spaces

1982 ◽  
Vol 32 (3) ◽  
pp. 332-338
Author(s):  
Bang-Yen Chen ◽  
Paul Verheyen
Keyword(s):  
Riemannian Manifold ◽  
Symmetric Spaces ◽  
Totally Umbilical ◽  
Totally Umbilical Submanifold ◽  
Totally Umbilical Submanifolds

AbstractA submanifold of a Riemannian manifold is called a totally umbilical submanifold if its first and second fundamental forms are proportional. In this paper we prove the following best possible result.

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