On the geometry of Riemannian warped product maps

In this paper, we begin by introducing Clairaut Riemannian warped product maps and establish the condition under which a regular curve becomes a geodesic. We obtain the conditions for a Riemannian warped product map to be Clairaut Riemannian warped product map followed by Ricci curvature. Further, we study the Ricci soliton structure on a Riemannian warped product manifold using curvature tensor. We examine the Bochner type formulae for Clairaut Riemannian warped product map and construct a supporting example. Furthermore, we extend the study to introduce and examine some geometric aspects of conformal Riemannian warped product maps. We derive the integral formula for scalar curvature of conformal Riemannian warped product map. Finally, we construct an example for conformal Riemannian warped product map.