×

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.
Reviewer: Radu Miron (Iaşi)

MSC:

53B20 Local Riemannian geometry
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
PDF BibTeX XML Cite
Full Text: EMIS