Hypersurfaces compactes dun fibr\'e vectoriel Riemannien \`a courbure moyenne prescrite

TL;DR

This paper investigates the existence of embeddings of sphere subbundles in Riemannian vector bundles with a specified mean curvature, extending geometric analysis in Riemannian geometry.

Contribution

It introduces conditions for embeddings of sphere subbundles with prescribed mean curvature in Riemannian vector bundles over compact manifolds.

Findings

Established existence criteria for such embeddings

Extended geometric analysis techniques to vector bundle settings

Provided new insights into curvature prescriptions in Riemannian geometry

Abstract

Let M be a compact Riemannian manifold without boundary and let E be a Riemannian vector bundle over M. If $\sigma$ denotes the sphere subbundle of E, we look for embeddings of $\sigma$ into E admitting a prescribed mean curvature.