Optimal inequalities for the normalizedδ-Casorati curvatures of submanifolds in Kenmotsu space forms

Abstract In this paper, we establish two sharp inequalities for the normalized δ -Casorati curvatures of submanifolds in a Kenmotsu space form, tangent to the structure vector field of the ambient space.Moreover, we show that in both cases the equality at all points characterizes the totally geodesic submanifolds.