Bi-slant Riemannian maps to Kenmotsu manifolds and some optimal inequalities

TL;DR

This paper introduces bi-slant Riemannian maps to Kenmotsu manifolds, explores their properties, and establishes various optimal inequalities involving curvature measures, expanding the understanding of geometric relations in this context.

Contribution

It defines bi-slant Riemannian maps to Kenmotsu manifolds and derives new curvature inequalities, generalizing existing concepts in differential geometry.

Findings

Derived curvature relations for the orthogonal complement of the map's range.

Established Chen-Ricci and DDVV inequalities for these maps.

Proved new optimal inequalities involving Casorati curvatures.

Abstract

In this paper, we introduce bi-slant Riemannian maps from Riemannian manifolds to Kenmotsu manifolds, which are the natural generalizations of invariant, anti-invariant, semi-invariant, slant, semi-slant and hemi-slant Riemannian maps, with nontrivial examples. We study these maps and give some curvature relations for $(rangeF_*)^\perp$. We construct Chen-Ricci inequalities, DDVV inequalities, and further some optimal inequalities involving Casorati curvatures from bi-slant Riemannian manifolds to Kenmotsu space forms.