Isotropic Riemannian submersions

Abstract

In this paper, we present the notion of isotropic submersions between Riemannian manifolds. We first give examples to illustrate this new notion. Then we express a characterization in terms of O’Neill’s tensor field T and examine certain relations between sectional curvatures of the total manifold and the base manifold. We also study λ-isotropic submersions with pointwise planar horizontal sections.