On the geometry of Clairaut warped product Riemannian maps

TL;DR

This paper introduces Clairaut warped product Riemannian maps, establishing conditions for geodesics and curvature, thereby advancing understanding of their geometric properties.

Contribution

It defines Clairaut warped product Riemannian maps and derives conditions for geodesics and curvature tensor, expanding the theoretical framework of Riemannian maps.

Findings

Conditions for geodesics of regular curves

Criteria for a warped product Riemannian map to be Clairaut

Explicit form of the curvature tensor

Abstract

In this paper, we introduce Clairaut warped product Riemannian maps. To study these kind of maps, first, we find the condition of geodesic of a regular curve. Then we obtain the conditions for a warped product Riemannian map to be Clairaut warped product Riemannian map. Further, we find the curvature tensor for this map.