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- Publisher
- Springer Journals
- Copyright
- Copyright © 2017 by Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Mathematics, general
- ISSN
- 0025-5874
- eISSN
- 1432-1823
- DOI
- 10.1007/s00209-017-1847-6
- Publisher site
- See Article on Publisher Site
Abstract
In this note, we use Chern’s magic form $$\Phi _k$$ Φ 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 $$L_k$$ 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 (Proc Am Math Soc 144:753–761, 2016) and Herzlich (Ann Henri Poincaré 17(12):3605–3617, 2016) very recently.
Journal
Mathematische Zeitschrift – Springer Journals
Published: Feb 27, 2017