Isotropic space form Riemannian submersions

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 3) into a space form N^n+p (? c) with constant? c sectional curvature, we demonstrate that the T -fundamental tensor of N^+p with respect to M^ is parallel if the mean curvature vector of M^ is parallel and the sectional curvature K of N^+p satisfies a given inequality. Accordingly, N^+p is a space form with lift.