Riemannian Manifolds with a semi-symmetric Metric Connection Satisfying Some Semisymmetry Conditions

Teatavaid semisümmeetrilisuse tingimusi rahuldavad Riemanni muutkonnad semi-sümmeetrilise meetrilise seostusega

Cengizhan Murathan ； Cihan Özgür

《Proceedings of the Estonian Academy of Sciences》 57卷4期 (2008/12) Pp. 210-216

並列摘要

We study Riemannian manifolds M admitting a semi-symmetric metric connection (The Symbol is abbreviated) such that the vector field U is a parallel unit vector field with respect to the Levi-Civita connection ▽. We prove that R•R=0 if and only if M is semisymmetric; if R•R=0 or R•R-R•R=0 or M is semisymmetric and R•R=0, then M is conformally flat and quasi-Einstein. Here R and R denote the curvature tensors of ▽ and (The Symbol is abbreviated), respectively.

並列關鍵字

Levi-Civita connection ； semi-symmetric metric connection ； conformally flat manifold ； quasi-Einstein manifold