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

Murathan C., ÖZGÜR C.

Proceedings of the Estonian Academy of Sciences, cilt.57, sa.4, ss.210-216, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 57 Sayı: 4
  • Basım Tarihi: 2008
  • Doi Numarası: 10.3176/proc.2008.4.02
  • Dergi Adı: Proceedings of the Estonian Academy of Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.210-216
  • Anahtar Kelimeler: Levi-Civita connection, semi-symmetric metric connection, conformally flat manifold, quasi-Einstein manifold, TORSION
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.