Golden Riemannian Submersions

Abstract

In this paper, we introduce the notion of golden Riemannian submersion between golden Riemannian manifolds. Here, we investigate the geometric properties of such a submersion and give some remarkable results. Also, we study the relations between the Ricci curvatures on the base manifold, target manifold and any fibre of golden Riemannian submersion and using these relations obtain two sharp inequalities. Moreover, we give some characterizations of golden Riemannian submersion whose total space admits a Ricci soliton with the horizontal or vertical potential field. Finally, we establish some examples of golden Riemannian submersions.