Notes on extended recurrent and extended quasi-recurrent manifolds.
On a class of Ricci-recurrent manifolds.
On some generalisation of recurrent manifolds.
On totally umbilical submanifolds of manifolds with certain recurrent condition imposed on the curvature tensor.
On conformally birecurrent Ricci-recurrent manifolds
Totally umbilical submanifolds in some semi-Riemannian manifolds
We investigate totally umbilical submanifolds in manifolds satisfying some curvature conditions of either recurrent or pseudosymmetry type in the sense of Ryszard Deszcz and derive the respective condition for submanifolds. We also prove some relations involving the mean curvature and the Weyl conformal curvature tensor of submanifolds. Some examples are discussed.
On totally umbilical submanifolds of conformally birecurrent manifolds
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