Second order parallel tensors on $S$ -manifolds and semi-parallel hypersurfaces of $S$ -space forms

Abstract

UDC 515.12
We study a second order parallel symmetric tensor in an $\mathcal{S}$-manifold and we deduce that there is no semi-parallel hypersurface in $\mathcal{S}$-space forms $\widetilde{M}^{2n+s}(c)$ with $c\neq s.$