Slant Riemannian maps to Kaehler manifolds

TL;DR

This paper introduces and studies slant Riemannian maps from Riemannian to almost Hermitian manifolds, generalizing several existing concepts, and explores their properties, harmonicity, and conditions for being totally geodesic.

Contribution

It defines slant Riemannian maps, provides characterizations, examples, and investigates their harmonicity and geodesic conditions, linking to pseudo horizontally weakly conformal maps.

Findings

Characterization of slant Riemannian maps

Conditions for harmonicity and total geodesicity

Relation to pseudo horizontally weakly conformal maps

Abstract

We introduce slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of slant immersions, invariant Riemannian maps and anti-invariant Riemannian maps. We give examples, obtain characterizations and investigate the harmonicity of such maps. We also obtain necessary and sufficient conditions for slant Riemannian maps to be totally geodesic. Moreover we relate the notion of slant Riemannian maps to the notion of pseudo horizontally weakly conformal maps which are useful for proving various complex-analytic properties of stable harmonic maps from complex projective space.