Chen–Ricci inequality for anti-invariant Riemannian submersions from conformal Kenmotsu space form

Abstract

Abstract The aim of this paper is twofold: first, we obtain various curvature inequalities which involve the Ricci and scalar curvatures of horizontal and vertical distributions of anti-invariant Riemannian submersion defined from conformal Kenmotsu space form onto a Riemannian manifold. Second, we obtain the Chen–Ricci inequality for the said Riemannian submersion. The equality cases of all the inequalities are studied. Moreover, these curvature inequalities are studied under two different cases: the structure vector field $$\xi $$ ξ being vertical or horizontal.

Keywords

• 53C12
• 53C25
• 53C40