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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-2-1,
author = {Ryszard Deszcz and Ma\l gorzata G\l ogowska and Marian Hotlo\'s and Leopold Verstraelen},
title = {On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {149-166},
zbl = {1050.53020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-2-1}
}
Ryszard Deszcz; Małgorzata Głogowska; Marian Hotloś; Leopold Verstraelen. On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms. Colloquium Mathematicae, Tome 96 (2003) pp. 149-166. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-2-1/