On 3-dimensional generalized (κ, μ)-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 (Journal Indexed in SCI Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 1
  • Publication Date: 2007
  • Title of Journal : Balkan Journal of Geometry and its Applications
  • Page Numbers: pp.122-134

Abstract

In the present study, we considered 3-dimensional generalized (κ, μ)-contact metric manifolds. We proved that a 3-dimensional generalized (κ, μ)-contact metric manifold is not locally φ-symmetric in the sense of Takahashi. However such a manifold is locally φ-symmetric provided that κ and μ are constants. Also it is shown that if a 3-dimensional generalized (κ, μ) -contact metric manifold is Ricci-symmetric, then it is a (κ, μ)-contact metric manifold. Further we investigated certain conditions under which a generalized (κ, μ)-contact metric manifold reduces to a (κ, μ)-contact metric manifold. Then we obtain several necessary and sufficient conditions for the Ricci tensor of a generalized (κ, μ)-contact metric manifold to be η-parallel. Finally, we studied Ricci-semisymmetric generalized (κ, μ)-contact metric manifolds and it is proved that such a manifold is either flat or a Sasakian manifold. © Balkan Society of Geometers, Geometry Balkan Press 2007.