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IMI/Publicaţii/BASM/Ediţii/BASM n.1(89), 2019/

On invariant submanifolds of S-manifolds

Authors: F. Mahi, M. Belkhelfa

Abstract

We consider invariant, pseudo-parallel and Ricci generalized pseudo-parallel submanifolds of $\mathcal{S}$-manifolds. We show that the submanifolds are totally geodesic under certain conditions. Also we study an invariant submanifold of $\mathcal{S}$-manifold satisfying $Q(\sigma,R)=0$ and $Q(S,\sigma)=0$, where $S$, $R$ and $\sigma$ are the Ricci tensor, curvature tensor and the second fundamental form respectively.

F. Mahi
Department of Exact Sciences, ENS of Mostaganem
Mostaganem 27000, Algeria
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M. Belkhelfa
Laboratory L. P. Q. 3M, Mustapha Stambouli University
Mascara 29000, Algeria
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