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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-2-8,
author = {Stanis\l aw Ewert-Krzemieniewski},
title = {Totally umbilical submanifolds in some semi-Riemannian manifolds},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {269-299},
zbl = {1191.53019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-2-8}
}
Stanisław Ewert-Krzemieniewski. Totally umbilical submanifolds in some semi-Riemannian manifolds. Colloquium Mathematicae, Tome 120 (2010) pp. 269-299. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-2-8/