scholarly journals Generic submanifolds of a locally conformal Kaehler manifold-II

1993 ◽  
Vol 16 (3) ◽  
pp. 557-564 ◽  
Author(s):  
M. Hasan Shahid ◽  
Kouei Sekigawa
Keyword(s):  
Generic Product ◽  
Kaehler Manifold ◽  
Totally Umbilical ◽  
Generic Submanifolds ◽  
Parallel Structures ◽  
Totally Umbilical Submanifolds ◽  
Locally Conformal

The purpose of this paper is to study generic submanifolds with parallel structures, generic product submanifolds and totally umbilical submanifolds of a locally conformal Kaehler manifold. Moreover, we give some examples of generic submanifolds of a locally conformal Kaehler manifold which are notCR-submanifolds.

scholarly journals On totally umbilicalCR-submanifolds of a Kaehler manifold

1993 ◽  
Vol 16 (2) ◽  
pp. 405-408
Author(s):  
M. A. Bashir
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Curvature Vector ◽  
Lens Space ◽  
Holomorphic Sectional Curvature ◽  
Mean Curvature Vector ◽  
Kaehler Manifold ◽  
Totally Umbilical ◽  
The Mean

LetMbe a compact3-dimensional totally umbilicalCR-submanifold of a Kaehler manifold of positive holomorphic sectional curvature. We prove that if the length of the mean curvature vector ofMdoes not vanish, thenMis either diffeomorphic toS3orRP3or a lens spaceLp,q3.

scholarly journals On Generic submanifolds of a locally conformal Kahler manifold with parallel canonical structures

1995 ◽  
Vol 18 (2) ◽  
pp. 331-340
Author(s):  
M. Hasan shahid ◽  
A. Sharfuddin
Keyword(s):  
Necessary Conditions ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Kahler Manifold ◽  
Generic Submanifolds ◽  
Locally Conformal Kähler ◽  
Generic Submanifold ◽  
Locally Conformal ◽  
Totally Real

The study ofCR-submanifolds of a Kähler manifold was initiated by Bejancu [1]. Since then many papers have appeared onCR-submanifolds of a Kähler manifold. Also, it has been studied that generic submanifolds of Kähler manifolds [2] are generalisations of holomorphic submanifolds, totally real submanifolds andCR-submanifolds of Kähler manifolds. On the other hand, many examplesC2of generic surfaces in which are notCR-submanifolds have been given by Chen [3] and this leads to the present paper where we obtain some necessary conditions for a generic submanifolds in a locally conformal Kähler manifold with four canonical strucrures, denoted byP,F,tandf, to have parallelP,Fandt. We also prove that for a generic submanifold of a locally conformal Kähler manifold,Fis parallel ifftis parallel.

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 TOTALLY UMBILICAL CR-SUBMANIFOLDS OF A NEARLY KAEHLER MANIFOLD

1996 ◽  
Vol 27 (2) ◽  
pp. 145-149
Author(s):  
S. H. KON ◽  
SIN-LENG TAN
Keyword(s):  
Kaehler Manifold ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Cr Submanifold ◽  
Nearly Kaehler Manifold ◽  
Totally Real ◽  
Cr Submanifolds

The geometry of a CR-submanifold in a Kaehler manifold has been extensively studied. B.Y . Chen has classified the totally umbilical CR-submanifolds of a Kaehler manifold and showed that they are either totally geodesic, or totally real or dim$(D^{\perp}) =1$. In this paper we show that such a result is also true in a nearly Kaehler manifold.

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
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