Chen-Ricci and Hineva Inequalities For Riemannian Submersions and Riemannian Maps With Applications

The Chen--Ricci inequality provides a sharp upper estimate for the Ricci curvature in terms of the ambient curvature and the squared mean curvature, whereas the Hineva inequality gives a complementary lower estimate. Although Chen--Ricci inequalities have been investigated for Riemannian submersions