Inequalities on Riemannian Warped Product Submersions for Vertical Casorati Curvatures

Abstract

The first and second authors introduced Riemannian warped product submersions and discussed interesting fundamental geometric properties of such submersions in Kupeli Erken and Murathan,. In the present paper, we extend this study to put light on the curvature properties of such submersions and then obtain optimal inequalities for Riemannian warped product submersions involving vertical Casorati curvatures. Also, we discuss under which conditions the equality case of inequality can hold with an example.