ISOTROPIC SPACE FORM RIEMANNIAN SUBMERSIONS

Abstract

We introduce the notion of isotropic space form submersions between Riemannian manifolds in this paper. We begin with a concrete example to demonstrate this new concept. We then characterize isotropic space form submersions in terms of O’Neill’s tensor field, T ̃ , and explore some relationships between the sectional curvatures of the base manifold and the total manifold. Particularly, considering an isotropic lift M ̃ (where l ≥ 3) into a space form N ̃ n+p( ̈c) with constant ̈c sectional curvature, We demonstrate that the T ̃-fundamental tensor of N ̃ l+p with respect to M ̃ is parallel if the mean curvature vector of M ̃ is parallel and the sectional curvature K ̃ of N ̃ l+p satisfies a given inequality. Accordingly, N ̃ l+p is a space form with lift.