The Gauss-Bonnet-Chern Center of Mass for Asymptotically Flat Manifolds

TL;DR

This paper introduces a new family of center of mass definitions for asymptotically flat manifolds, complementing existing Gauss-Bonnet-Chern masses, using double forms formalism for clear proofs.

Contribution

It proposes a novel family of center of mass concepts that extend Gauss-Bonnet-Chern masses, with a unified proof framework applicable to known asymptotic invariants.

Findings

Existence and well-definedness of the new center of mass are established.

The formalism of double forms simplifies proofs and applies broadly.

The new definitions complement existing mass concepts in geometric analysis.

Abstract

In this paper we introduce a family of center of masses that complement the definition of the family of Gauss-Bonnet-Chern masses by Ge-Wang-Wu and Li-Nguyen. In order to prove the existence and the well-definedness of the center of mass, we use the formalism of double forms of Kulkarni and Labbi. This allows for transparent conceptual proofs, which apply to all known cases of asymptotic invariants of asymptotically flat manifolds.