Some theorems on conformally quasi-recurrent manifolds


Mileva Prvanović




A conformally quasi-recurrent manifold is an $n$-dimensional $(n>3)$ Riemannian manifold whose conformal curvature tensor satisfies the condition (1.2), where $\nabla$ is the operator of covariant differentiation. It is proved that if $a_1$ is a gradient vector field, such a manifold can be conformally related to the conformally symmetric one (i.e. to the manifold satisfying $\nabla_sC_{hijk}=0$). Using this fact, it is proved that many properties of conformally symmetric manifolds can be generalized in such a manner that they hold good for conformally quasi-recurrent manifolds too (In which $a_1$ is a gradient vector field). Also, some properties of general quasi-recurrent manifolds are obtained.