The Pestov identity on the frame bundle and associated homogeneous fibrations

TL;DR

This paper establishes a global Pestov identity on the frame bundle of a Riemannian manifold and related fibrations, providing a streamlined proof of the Pestov identity on the unit tangent bundle, with implications for geometric analysis.

Contribution

It introduces a global Pestov identity on the frame bundle and associated fibrations, offering a concise proof for the identity on the unit tangent bundle.

Findings

Proves a global Pestov identity on the frame bundle.

Derives identities on associated homogeneous fibrations.

Provides a simplified proof of the Pestov identity on the unit tangent bundle.

Abstract

In this short note, we prove a global Pestov identity on the (orthonormal) frame bundle of a Riemannian manifold and deduce similar identities on associated homogeneous fibrations. As a particular example, this provides a concise proof of the Pestov identity on the unit tangent bundle of the manifold.