Geodesic
Totally umbilical submanifolds in some semi-Riemannian manifolds
Stanisław Ewert-Krzemieniewski1
1 School of Mathematics West Pomeranian University of Technology Al. Piastów 17 70-310 Szczecin, Poland
Colloquium Mathematicum, Tome 119 (2010) no. 2, pp. 269-299 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm119-2-8
Keywords: investigate totally umbilical submanifolds manifolds satisfying curvature conditions either recurrent pseudosymmetry type sense ryszard deszcz derive respective condition submanifolds prove relations involving mean curvature weyl conformal curvature tensor submanifolds examples discussed

Stanisław Ewert-Krzemieniewski 1

1 School of Mathematics West Pomeranian University of Technology Al. Piastów 17 70-310 Szczecin, Poland 
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Stanisław Ewert-Krzemieniewski. Totally umbilical submanifolds in some
 semi-Riemannian manifolds. Colloquium Mathematicum, Tome 119 (2010) no. 2, pp. 269-299. doi: 10.4064/cm119-2-8

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