Chen-Ricci inequality for anti-invariant Riemannian submersions from conformal Kenmotsu space form (Q6611211)

Riemannian invariants are of primary importance in Riemannian geometry. These invariants determine the extrinsic and intrinsic properties of Riemannian manifolds which in turn affect the behavior of the manifold in general form. The relationship between intrinsic and extrinsic invariants was established by \textit{B.-Y. Chen} [Arch. Math. 60, No. 6, 568--578 (1993; Zbl 0811.53060)]. He established a link between main intrinsic invariants and main extrinsic invariants in the form of some inequalities. Chen also established a relationship between the squared mean curvature and Ricci curvature of a submanifold in the form of an inequality.\N\NIn this paper the authors prove the Chen-Ricci inequality for anti-invariant Riemannian submersions from conformal Kenmotsu space forms and study the equality cases of these inequalities. Moreover, these curvature inequalities are studied in two different cases: the structure vector field \(\xi\) being vertical or horizontal. The authors also 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.