Optimal inequalities for Riemannian maps and Riemannian submersions involving Casorati curvatures

Abstract

Riemannian maps are generalizations of well-known notions of isometric immersions and Riemannian submersions. Most optimal inequalities on submanifolds in various ambient spaces are driven from isometric immersions. The main aim of this paper is to obtain optimal inequalities for Riemannian maps to space forms, as well as for Riemannian submersions from space forms, involving Casorati curvatures.