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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Communicated by Piotr T. Chrusciel.
Y. Y. Li was partially supported by NSF Grant DMS-1203961.
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Li, Y.Y., Nguyen, L. A Generalized Mass Involving Higher Order Symmetric Functions of the Curvature Tensor. Ann. Henri Poincaré 14, 1733–1746 (2013). https://doi.org/10.1007/s00023-013-0230-3
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DOI: https://doi.org/10.1007/s00023-013-0230-3