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, cilt.12, sa.1, ss.122-134, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 1
  • Basım Tarihi: 2007
  • Dergi Adı: BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.122-134
  • Anahtar Kelimeler: generalized (kappa, mu)-contact manifolds, locally phi-symmetric, eta-parallel Ricci tensor, Sasakian manifold
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.