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, T̃ , and explore some relationships between the sectional curvatures of the base manifold and the total manifold. Particularly, considering an isotropic lift M̃^{} (where ≥ 3 ) into a space form Ñⁿ⁺ᵖ({?c}) with constant ?c sectional curvature, we demonstrate that the T̃ -fundamental tensor of Ñ⁺ᵖ with respect to M̃^{} is parallel if the mean curvature vector of M̃^{} is parallel and the sectional curvature K̃ of Ñ⁺ᵖ satisfies a given inequality. Accordingly, Ñ⁺ᵖ is a space form with lift.