A Bonnet theorem for submanifolds into rotational hypersurfaces

TL;DR

This paper extends the fundamental theorem of submanifolds to include target manifolds with warped product structures, broadening the understanding of submanifold geometry in such contexts.

Contribution

It introduces a Bonnet-type theorem for submanifolds into rotational hypersurfaces, generalizing classical results to warped product target manifolds.

Findings

Established a fundamental theorem for submanifolds in warped target manifolds

Provided conditions for the existence and uniqueness of such submanifolds

Extended classical submanifold theory to new geometric settings

Abstract

In this work, we prove a version of the fundamental theorem of submanifolds to target manifolds with warped structure.