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arXiv · 1211.3676

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

YanYan Li·Luc Nguyen
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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 $σ_k$ 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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YanYan Li, Luc Nguyen. 2012-11-16. A generalized mass involving higher order symmetric function of the curvature tensor. https://doi.org/10.1007/s00023-013-0230-3

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