Totally umbilical submanifolds in some semi-Riemannian manifolds

Stanisław Ewert-Krzemieniewski. "Totally umbilical submanifolds in some semi-Riemannian manifolds." Colloquium Mathematicae 119.2 (2010): 269-299. <http://eudml.org/doc/283927>.

@article{StanisławEwert2010,
abstract = {We investigate totally umbilical submanifolds in manifolds satisfying some curvature conditions of either recurrent or pseudosymmetry type in the sense of Ryszard Deszcz and derive the respective condition for submanifolds. We also prove some relations involving the mean curvature and the Weyl conformal curvature tensor of submanifolds. Some examples are discussed.},
author = {Stanisław Ewert-Krzemieniewski},
journal = {Colloquium Mathematicae},
keywords = {totally umbilical submanifold; Weyl tensor; conformal curvature; recurrent; pseudosymmetry},
language = {eng},
number = {2},
pages = {269-299},
title = {Totally umbilical submanifolds in some semi-Riemannian manifolds},
url = {http://eudml.org/doc/283927},
volume = {119},
year = {2010},
}

TY - JOUR
AU - Stanisław Ewert-Krzemieniewski
TI - Totally umbilical submanifolds in some semi-Riemannian manifolds
JO - Colloquium Mathematicae
PY - 2010
VL - 119
IS - 2
SP - 269
EP - 299
AB - We investigate totally umbilical submanifolds in manifolds satisfying some curvature conditions of either recurrent or pseudosymmetry type in the sense of Ryszard Deszcz and derive the respective condition for submanifolds. We also prove some relations involving the mean curvature and the Weyl conformal curvature tensor of submanifolds. Some examples are discussed.
LA - eng
KW - totally umbilical submanifold; Weyl tensor; conformal curvature; recurrent; pseudosymmetry
UR - http://eudml.org/doc/283927
ER -