NON-DEGENERATE HYPERSURFACES OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

YÜCESAN A., YAŞAR E.

MATHEMATICAL REPORTS, vol.14, no.2, pp.209-219, 2012 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2012
  • Journal Name: MATHEMATICAL REPORTS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.209-219
  • Süleyman Demirel University Affiliated: Yes

Abstract

We consider a non-degenerate hypersurface of a semi-Riemannian manifold with a semi-symmetric non-metric connection. We obtain a relation between the Ricci and the scalar curvatures of a semi-Riemannian manifold and of its non-degenerate hypersurface with respect to a semi-symmetric non-metric connection. We also show that the Ricci tensor of a non-degenerate hypersurface of a semi-Riemannian space form admitting a semi-symmetric non-metric connection is symmetric, but not parallel. Finally, we get the conditions under which a non-degenerate hypersurface with a semi-symmetric non-metric connection is projectively flat.