A Generalized Mass Involving Higher Order Symmetric Functions of the Curvature Tensor |
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| Authors: | Yan Yan Li Luc Nguyen |
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| Affiliation: | 1. Mathematics Department, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ, 08854, USA
2. Mathematics Department, Princeton University, Fine Hall,Washington Road, Princeton, NJ, 085440, USA
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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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