## Conformally symmetric manifolds and quasi conformally recurrent Riemannian manifolds.(English)Zbl 1226.53007

A classical theorem about conformally symmetric Riemannian metrics is as follows: An $$n$$ $$(\geq 4)$$ dimensional conformally symmetric manifold is conformally flat or locally symmetric. Miyazawa proved this statement with the extra assumption of $$n>4$$ while Derdzinski and Roter give a proof of the general case $$n>3$$. The present work gives a new proof and provides extensions of it to quasi-conformal symmetric and quasi-conformal recurrent Riemannian manifolds.