On 3-dimensional generalized (kappa, mu)-contact metric manifolds


Shaikh A. A., Arslan K., Murathan C., Baishya K. K.

BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS, vol.12, no.1, pp.122-134, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 1
  • Publication Date: 2007
  • Journal Name: BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.122-134
  • Keywords: generalized (kappa, mu)-contact manifolds, locally phi-symmetric, eta-parallel Ricci tensor, Sasakian manifold
  • Bursa Uludag University Affiliated: Yes

Abstract

In the present study, we considered 3-dimensional generalized (kappa, mu)-contact metric manifolds. We proved that a 3-dimensional generalized (kappa, mu)-contact metric manifold is not locally phi-symmetric in the sense of Takahashi. However such a manifold is locally phi-symmetric provided that kappa and mu are constants. Also it is shown that if a 3-dimensional generalized (kappa, mu) -contact metric manifold is Ricci-symmetric, then it is a (kappa, mu)-contact metric manifold. Further we investigated certain conditions under which a generalized (kappa, mu)-contact metric manifold reduces to a (kappa, mu)-contact metric manifold. Then we obtain several necessary and sufficient conditions for the Ricci tensor of a generalized (kappa, mu)-contact metric manifold to be eta-parallel. Finally, we studied Ricci-semisymmetric generalized (kappa, mu)-contact metric manifolds and it is proved that such a manifold is either flat or a Sasakian manifold.