On generalized recurrent Riemannian manifolds

Arslan K., De U. C. , Murathan C. , Yildiz A.

Acta Mathematica Hungarica, vol.123, pp.27-39, 2009 (Journal Indexed in SCI Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 123
  • Publication Date: 2009
  • Doi Number: 10.1007/s10474-008-8049-y
  • Title of Journal : Acta Mathematica Hungarica
  • Page Numbers: pp.27-39
  • Keywords: generalized recurrent manifold, concirculary recurent manifold, quasi-Einstein manifold, Ricci-semisymmetry, CLASSIFICATION

Abstract

The object of the present paper is to study a type of Riemannian manifolds called generalized recurrent manifolds. We have constructed two concrete examples of such a manifold whose scalar curvature is non-zero non-constant. Some other properties have been considered. Among others it is shown that on a generalized recurrent manifold with constant scalar curvature, Weyl-semisymmetry and semisymmetry are equivalent. Sufficient condition for a generalized recurrent manifold to be a special quasi Einstein manifold is obtained. © 2008 Springer Science+Business Media B.V.