Clairaut slant Riemannian maps to K\"ahler manifolds

Author:

Jyoti Yadav, Gauree Shanker, Murat Polat

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG)

journal:

date:

2023-06-13 16:00:00

Abstract

The aim of this article is to describe the idea of Clairaut slant Riemannian maps from Riemannian manifolds to K\"ahler manifolds. First, for the slant Riemannian map, we obtain the necessary and sufficient conditions for a curve to be a geodesic on the base manifold. Further, we find the necessary and sufficient conditions for the slant Riemannian map to be a Clairaut slant Riemannian map; for Clairaut slant Riemannian map to be totally geodesic; for the base manifold to be a locally product manifold. Further, we obtain the necessary and sufficient condition for the integrability of range of derivative map. Also, we investigate the harmonicity of Clairaut slant Riemannian map. Finally, we get two inequalities in terms of second fundamental form of a Clairaut slant Riemannian map and check the equality case.

PDF: Clairaut slant Riemannian maps to K\"ahler manifolds.pdf