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On invariant submanifolds of $S$-manifolds

Fatiha Mahi^a, Mohamed Belkhelfa<sup>b

a</sup> Department of Exact Sciences, ENS of Mostaganem, Mostaganem 27000, Algeria
^b Laboratory L. P. Q. 3M, Mustapha Stambouli University, Mascara 29000, Algeria

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.

Keywords and phrases: $\mathcal{S}$-manifold, invariant submanifold, totally geodesic, pseudo-parallel, Ricci generalized pseudo-parallel.

MSC: 53C25, 53C15

Received: 19.02.2018

Language: English