Chern's magic form and the Gauss-Bonnet-Chern mass

Abstract

In this note, we use Chern's magic form ${\Phi }_k$ in his famous proof of the Gauss-Bonnet theorem to define a mass for asymptotically flat manifolds. It turns out that the new defined mass is equivalent to the one that we introduced recently by using the Gauss-Bonnet-Chern curvature $L_k$. Moreover, this equivalence implies a simple proof of the equivalence between the ADM mass and the intrinsically defined mass via the Ricci tensor, which was reconsidered by Miao-Tam \cite{MT} and Herzlich \cite{H} very recently.

11 pages

References in corpus (1)

• Evaluation of the ADM mass and center of mass via the Ricci tensor

Cited by in corpus (2)

• Quasi-local mass integrals and the total mass
• Some functionals on compact manifolds with boundary