Curvature estimates for submanifolds in warped products

TL;DR

This paper provides curvature estimates for submanifolds immersed in warped product spaces, extending to cases involving Riemannian submersions, enhancing understanding of geometric properties in these contexts.

Contribution

It introduces new curvature bounds for submanifolds in warped products and extends these results to submanifolds in Riemannian submersions.

Findings

Curvature estimates for cylindrically bounded submanifolds in warped products.

Extensions of curvature bounds to submanifolds of Riemannian submersions.

Enhanced understanding of intrinsic and extrinsic curvature relations.

Abstract

We give estimates on the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of the total space of a Riemannian submersion.