Geodesic
On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms
Ryszard Deszcz 1   ; Małgorzata Głogowska 1   ; Marian Hotloś 2   ; Leopold Verstraelen 3
1 Department of Mathematics Agricultural University of Wrocław Grunwaldzka 53 50-357 Wrocław, Poland
2 Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
3 Department of Mathematics Katholieke Universiteit Leuven Celestijnenlaan 200B B-3001 Leuven, Belgium
Colloquium Mathematicum, Tome 96 (2003) no. 2, pp. 149-166 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm96-2-1
Keywords: solutions ryan problem investigations curvature properties cartan hypersurfaces ricci pseudosymmetric hypersurfaces lead curvature identities holding every hypersurface isometrically immersed semi riemannian space form these identities under assumptions rises generalized einstein metric conditions investigate hypersurfaces satisfying curvature conditions

Ryszard Deszcz  1   ; Małgorzata Głogowska  1   ; Marian Hotloś  2   ; Leopold Verstraelen  3

1 Department of Mathematics Agricultural University of Wrocław Grunwaldzka 53 50-357 Wrocław, Poland
2 Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
3 Department of Mathematics Katholieke Universiteit Leuven Celestijnenlaan 200B B-3001 Leuven, Belgium 
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     title = {On some generalized {Einstein} metric
 conditions on hypersurfaces
 in {semi-Riemannian} space forms},
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     doi = {10.4064/cm96-2-1},
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 conditions on hypersurfaces
 in semi-Riemannian space forms
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 conditions on hypersurfaces
 in semi-Riemannian space forms
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Ryszard Deszcz; Małgorzata Głogowska; Marian Hotloś; Leopold Verstraelen. On some generalized Einstein metric
 conditions on hypersurfaces
 in semi-Riemannian space forms. Colloquium Mathematicum, Tome 96 (2003) no. 2, pp. 149-166. doi: 10.4064/cm96-2-1

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