A family of asymptotically hyperbolic manifolds with arbitrary energy-momentum vectors
A family of asymptotically hyperbolic manifolds with arbitrary energy-momentum vectors
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具有任意能量动量向量的渐近双曲流形族
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Julien Cortier
中科院分区：
文献类型：
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作者：
Julien Cortier
利用幂级数方法构造了一类以双曲空间为模型的Yamabe方程的非径向解。结果，我们得到了一族渐近双曲度量，具有球面共形无穷大，标量曲率大于或等于−n（n − 1），但它们是先验不完备的。此外，Rn+1的任何向量由一族的一个合适度量的能量动量向量执行。特别是，当人们去掉完备性假设时，它们可以为正能量-动量定理提供反例。
A family of non-radial solutions to the Yamabe equation, modeled on the hyperbolic space, is constructed using power series. As a result, we obtain a family of asymptotically hyperbolic metrics, with spherical conformal infinity, with scalar curvature greater than or equal to −n(n − 1), but which are a priori not complete. Moreover, any vector of Rn+1 is performed by an energy-momentun vector of one suitable metric of this family. They can in particular provide counter-examples to the positive energy-momentum theorem when one removes the completeness assumption.