The aim of this paper is to introduce Clairaut conformal submersion between Riemannian manifolds. First, we find necessary and sufficient conditions for a regular curve to be geodesic on the total and base manifold of conformal submersion. Further, we find necessary and sufficient conditions for conformal submersions to be Clairaut conformal submersions. Moreover, we find a necessary and sufficient condition for a Clairaut conformal submersion to be harmonic. Finally, we give two non-trivial examples of Clairaut conformal submersion. Out of them, one is given by using doubly warped product, and another one is given by verifying main result of the paper.
In this paper, we study conformal submersions from Ricci solitons to Riemannian manifolds. First, we study some properties of O' Neill tensor A, which are changed in the case of conformal submersion. We also find a necessary and sufficient condition for conformal submersion to be totally geodesic and calculate Ricci tensors for such map with different conditions. Further, we consider conformal submersion F : M → N from a Ricci soliton to a Riemannian manifold and obtain necessary conditions for fibers of F and base manifold N to be Ricci soliton, almost Ricci soliton and Einstein. Moreover, we find necessary conditions for a vector field and it's horizontal lift to be conformal on N and (KerF * ) ⊥ , respectively. Also, we calculate the scalar curvature of Ricci soliton M . Finally, we obtain a necessary and sufficient condition for F to be harmonic.
No abstract
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.