Bounded geometry and leaves

TL;DR

This paper proves that any complete connected Riemannian manifold with bounded geometry can be embedded as a leaf with trivial holonomy in a compact Riemannian foliated space, linking geometric bounds to foliation theory.

Contribution

It establishes a universal embedding result for bounded geometry manifolds into compact foliated spaces as leaves with trivial holonomy.

Findings

Any bounded geometry manifold can be realized as a leaf in a compact foliated space.

The embedding preserves the Riemannian structure and trivial holonomy.

Provides a new connection between bounded geometry and foliation theory.

Abstract

The main theorem states that any complete connected Riemannian manifold of bounded geometry can be isometrically realized as a leaf with trivial holonomy in a compact Riemannian foliated space.