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eISSN 0454-8124
pISSN 1225-6951

### Original Article

Kyungpook Mathematical Journal 2008; 48(2): 183-194

Published online June 23, 2008

We prove that totally umbilical submanifold $M$ of an extended quasi-recurren manifold is also extended quasi-recurrent. If, moreover, $M$ is conformally flat then, locally, $M$ is isometric to the manifold with known metric. Some curvature properties of such submanifold are investigated. Making use of these results we shall prove the existence of totally umbilical submanifold being pseudosymmetric in the sense of Ryszard Deszcz and satisfying some other curvature conditions.