B. Y. Chen-Ricci inequalities for anti-invariant Riemannian submersions in Kenmotsu space forms

Abstract

AbstractThe aim of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of anti-invariant Riemannian submersions in Kenmotsu space forms $$K_{s}(\varepsilon )$$ K s ( ε ) . We give non-trivial examples for anti-invariant Riemannian submersions, investigate some curvature relations between the total space and fibres according to vertical and horizontal cases of $$\xi $$ ξ . Moreover, we acquire Chen-Ricci inequalities on the $$\ker \vartheta _{*}$$ ker ϑ ∗ and $$(\ker \vartheta _{*})^{\bot }$$ ( ker ϑ ∗ ) ⊥ distributions for anti-invariant Riemannian submersions from Kenmotsu space forms according to vertical and horizontal cases of $$\xi $$ ξ .