Integral curvature and topological obstructions for submanifolds

TL;DR

This paper establishes integral curvature bounds for compact Riemannian manifolds that enable isometric immersions into Euclidean spaces with low codimension, linking geometric properties to topological invariants.

Contribution

It introduces new integral curvature bounds that relate the geometry of manifolds to their topological Betti numbers for low codimension immersions.

Findings

Integral curvature bounds depend on Betti numbers.

Conditions for isometric immersions into Euclidean space.

Connections between curvature and topology.

Abstract

We provide integral curvature bounds for compact Riemannian manifolds that allow isometric immersions into a Euclidean space with low codimension in terms of the Betti numbers.