The Pestov Identity on the Frame Bundle and Associated Homogeneous Fibrations

Key Points

• The aim is to establish a global Pestov identity on the frame bundle of Riemannian manifolds and its implications for homogeneous fibrations.
• Proved the global Pestov identity on the orthonormal frame bundle of a Riemannian manifold.
• Derived similar identities for associated homogeneous fibrations.
• Provided a concise proof of the Pestov identity on the unit tangent bundle as an application.
• Confirmed the Pestov identity on the frame bundle, enhancing understanding of geometric properties.
• Demonstrated the relationships between frame bundles and homogeneous fibrations.
• Illustrated the effectiveness of the proofs through the example of the unit tangent bundle.