Some properties of a quarter symmetric metric connection on a Riemannian manifold. (English) Zbl 0747.53021

Mukhopadhyay, S.; Roy, A. K.; Barua, B.

Soochow J. Math. 17, No. 2, 205-211 (1991).

Quarter symmetric connections on a differentiable manifold have been defined by R. S. Mishra [Structures on a differentiable manifold and their applications (1984; Zbl 0546.53026)]. In this paper the authors study the necessary and sufficient conditions for the conformal curvature tensor or the projective curvature tensor of a quarter symmetric, metric connection to be equal to the conformal curvature tensor or the projective curvature tensor of the Levi-Civita connection on a Riemannian manifold.

Reviewer: S.Ianus (Bucureşti)

MSC:

53C05

Connections (general theory)

Keywords:

projective curvature tensor; conformal curvature tensor

Citations:

Zbl 0546.53026