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SEMI-RIEMANNIAN SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

Yucesan, Ahmet;Yasar, Erol

  • Received : 2011.08.02
  • Published : 2012.10.31

Abstract

We study some properties of a semi-Riemannian submanifold of a semi-Riemannian manifold with a semi-symmetric non-metric connection. Then, we prove that the Ricci tensor of a semi-Riemannian submanifold of a semi-Riemannian space form admitting a semi-symmetric non-metric connection is symmetric but is not parallel. Last, we give the conditions under which a totally umbilical semi-Riemannian submanifold with a semi-symmetric non-metric connection is projectively flat.

Keywords

semi-symmetric non-metric connection;Levi-Civita connection;semi-Riemannian submanifold;Ricci tensor;projectively flat

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