A Generalized Mass Involving Higher Order Symmetric Functions of the Curvature Tensor

Yan Yan Li; Luc Nguyen

doi:10.1007/s00023-013-0230-3

A Generalized Mass Involving Higher Order Symmetric Functions of the Curvature Tensor

Yan Yan Li, Luc Nguyen

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1733-1746
Number of pages	14
Journal	Annales Henri Poincare
Volume	14
Issue number	7
DOIs	https://doi.org/10.1007/s00023-013-0230-3
State	Published - Nov 2013

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Nuclear and High Energy Physics
Mathematical Physics

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10.1007/s00023-013-0230-3

Cite this

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title = "A Generalized Mass Involving Higher Order Symmetric Functions 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 σk 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.",

author = "Li, {Yan Yan} and Luc Nguyen",

note = "Funding Information: Y. Y. Li was partially supported by NSF Grant DMS-1203961.",

year = "2013",

month = nov,

doi = "10.1007/s00023-013-0230-3",

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AU - Nguyen, Luc

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PY - 2013/11

Y1 - 2013/11

N2 - 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 σk 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.

AB - 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 σk 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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JO - Annales Henri Poincare

JF - Annales Henri Poincare

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ER -

A Generalized Mass Involving Higher Order Symmetric Functions of the Curvature Tensor

Abstract

All Science Journal Classification (ASJC) codes

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