Semi-slant Riemannian maps

TL;DR

This paper introduces semi-slant Riemannian maps from almost Hermitian to Riemannian manifolds, exploring their geometric properties, conditions for harmonicity and total geodesicity, and providing illustrative examples.

Contribution

It generalizes existing concepts of slant submersions and Riemannian maps, establishing new theoretical results and conditions for semi-slant Riemannian maps.

Findings

Conditions for integrability of distributions

Criteria for harmonicity and total geodesicity

Decomposition theorems for semi-slant Riemannian maps

Abstract

As a generalization of slant submersions (Sahin, 2011), semi-slant submersions (Park and Prasad), and slant Riemannian maps (Sahin), we define the notion of semi-slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We study the integrability of distributions, the geometry of fibers, the harmonicity of such maps, etc. We also find a condition for such maps to be totally geodesic and investigate some decomposition theorems. Moreover, we give examples.