A New Class of Slant Submanifolds in Generalized Sasakian Space Forms

Abstract

In this paper, we introduce the notion of $$*$$-slant submanifold as that slant submanifold whose second fundamental form satisfies the equality case of an inequality between its mean curvature and its scalar curvature. In addition to that, we give several interesting examples about these submanifolds. Finally, we obtain the Ricci curvature for a $$*$$-slant submanifold depending on the mean curvature vector and we give lower and upper bounds for the Ricci curvature.