On hypercylinders in conformally symmetric manifolds

Ryszard Deszcz

Abstract: {\bf Abstract}. Hypercylinders in conformally symmetric manifolds are considered. The main result is the following theorem: Let $(M,g)$ be a hypercylinder in a parabolic essentially conformally symmetric manifold $(N,\widetilde g)$, $\dim N\ge 5$ and let $\widetolde U$ be the subset od $N$ consisting of all points of $N$ at which the Ricci tensor $\widetilde S$ of $(N,\widetilde g)$ is not recurrent. If $\widetilde U\cap M$ is a dense subset of $M$, then $(M,g)$ is a conformally recurrent manifold.

Classification (MSC2000): 53B25, 53B20

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