On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms

Ryszard Deszcz, et al. "On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms." Colloquium Mathematicae 96.2 (2003): 149-166. <http://eudml.org/doc/285324>.

@article{RyszardDeszcz2003,
abstract = {Solutions of the P. J. Ryan problem as well as investigations of curvature properties of Cartan hypersurfaces and Ricci-pseudosymmetric hypersurfaces lead to curvature identities holding on every hypersurface M isometrically immersed in a semi-Riemannian space form. These identities, under some assumptions, give rises to new generalized Einstein metric conditions on M. We investigate hypersurfaces satisfying such curvature conditions.},
author = {Ryszard Deszcz, Małgorzata Głogowska, Marian Hotloś, Leopold Verstraelen},
journal = {Colloquium Mathematicae},
keywords = {Einstein manifold; quasi-Einstein manifold; pseudosymmetry type manifold; warped product; hypersurface; Ryan problem},
language = {eng},
number = {2},
pages = {149-166},
title = {On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms},
url = {http://eudml.org/doc/285324},
volume = {96},
year = {2003},
}

TY - JOUR
AU - Ryszard Deszcz
AU - Małgorzata Głogowska
AU - Marian Hotloś
AU - Leopold Verstraelen
TI - On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms
JO - Colloquium Mathematicae
PY - 2003
VL - 96
IS - 2
SP - 149
EP - 166
AB - Solutions of the P. J. Ryan problem as well as investigations of curvature properties of Cartan hypersurfaces and Ricci-pseudosymmetric hypersurfaces lead to curvature identities holding on every hypersurface M isometrically immersed in a semi-Riemannian space form. These identities, under some assumptions, give rises to new generalized Einstein metric conditions on M. We investigate hypersurfaces satisfying such curvature conditions.
LA - eng
KW - Einstein manifold; quasi-Einstein manifold; pseudosymmetry type manifold; warped product; hypersurface; Ryan problem
UR - http://eudml.org/doc/285324
ER -