A generalized mass involving higher order symmetric function of the curvature tensor

Abstract

We define a generalized mass for asymptotically flat manifolds using some higher order symmetric function of the curvature tensor. This mass is non-negative when the manifold is locally conformally flat and the ${\sigma }_k$ curvature vanishes at infinity. In addition, with the above assumptions, if the mass is zero, then, near infinity, the manifold is isometric to a Euclidean end.

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References in corpus (1)

• Masse des opérateurs GJMS

Cited by in corpus (4)

• A ${\sigma }_2$ Penrose inequality for conformal asymptotically hyperbolic 4-discs
• Chern's magic form and the Gauss-Bonnet-Chern mass
• The Gauss-Bonnet-Chern Center of Mass for Asymptotically Flat Manifolds
• The GBC mass for asymptotically hyperbolic manifolds