On weakly conformally symmetric manifolds. (English) Zbl 1224.53033

Shaikh, A. A.; Shahid, M. Hasan; Hui, Shyamal Kumar

Mat. Vesn. 60, No. 4, 269-284 (2008).

A weakly conformally symmetric manifold is a Riemannian manifold whose covariant derivative of its Weyl conformal curvature tensor \(C\) satisfies certain generalization of recurrence relation. The authors show that an Einstein weakly conformally symmetric manifold reduces to a weakly symmetric manifold. They also consider transformations of a weakly conformally symmetric manifold in a manifold of the same type. Several examples of weakly conformally symmetric manifolds with non-vanishing scalar curvature are constructed.

Reviewer: Neda Bokan (Beograd)

MSC:

53B20	Local Riemannian geometry
53B35	Local differential geometry of Hermitian and Kählerian structures
53B05	Linear and affine connections

Keywords:

conformal curvature tensor; conformal transformation; scalar curvature