INEQUALITIES INVOLVING k-CHEN INVARIANTS FOR SUBMANIFOLDS OF RIEMANNIAN PRODUCT MANIFOLDS

Abstract

Abstract:An optimal inequality involving the scalar curvatures, the meancurvature and the k-Chen invariant is established for Riemannian submanifolds. Particular cases of this inequality is reported. Furthermore, this inequality is investigated on submanifolds, namely slant, F-invariant and F-antiinvariant submanifolds of an almost constant curvature manifold.