Riemannian manifolds with a semi-symmetric metric connection satisfying some semisymmetry conditions


Murathan C. , ÖZGÜR C.

Proceedings of the Estonian Academy of Sciences, vol.57, no.4, pp.210-216, 2008 (Journal Indexed in SCI Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 57 Issue: 4
  • Publication Date: 2008
  • Doi Number: 10.3176/proc.2008.4.02
  • Title of Journal : Proceedings of the Estonian Academy of Sciences
  • Page Numbers: pp.210-216
  • Keywords: Levi-Civita connection, semi-symmetric metric connection, conformally flat manifold, quasi-Einstein manifold, TORSION

Abstract

We study Riemannian manifolds M admitting a semi-symmetric metric connection _̃t4 such that the vector field U is a parallel unit vector field with respect to the Levi-Civita connection ▽. We prove that R·R̃ = 0 if and only if M is semisymmetric; if R̃·R = 0 or R̃·R̃ - R̃·R = 0 or M is semisymmetric and R̃·R̃ = 0, then M is conformally flat and quasi-Einstein. Here R and R̃ denote the curvature tensors of ▽ and _̃t4, respectively.