Clairaut conformal hemi-slant submersions from Kahler manifolds

Abstract

In this paper, we introduce and study Clairaut conformal hemi-slant submersions from K\"ahler manifolds onto Riemannian manifolds. This class of maps combines the geometry of Clairaut conformal submersions with the hemi-slant decomposition of the vertical distribution in the almost Hermitian manifolds. We first establish a characterization theorem for Clairaut conformal hemi-slant submersions in terms of the geodesic behavior on the total manifold, the mean curvature of the fibers, and the behavior of the dilation along the fibers. We then derive equivalent formulations of the Clairaut condition adapted to the slant and anti-invariant components of the vertical distribution and obtain refined decompositions of the Clairaut relation and the harmonicity condition with respect to the hemi-slant splitting. Furthermore, we investigate the stability of the Clairaut conformal hemi-slant structure under conformal deformations of the total metric. We also study curvature properties of such submersions and obtain vertical sectional, scalar and Ricci curvature decomposition formulas compatible with the hemi-slant structure. In particular, the vertical curvature is decomposed into its slant, anti-invariant and mixed components, revealing the geometric influence of the hemi-slant splitting on the Clairaut and harmonic structures. Finally, we provide an explicit nontrivial example illustrating the theory.