李群上的负曲左不变度量
Negatively curved left-invariant metrics on Lie groups
摘要：
我们讨论了负弯曲的齐性空间，它允许一个单传递的等距群，或者等价地，李群上的负弯曲的左不变度量。负弯曲的空间具有非常丰富和多样的结构，从数学和物理的角度来看都很有趣。除了给出具有负Ricci曲率标量的左不变度量的一般准则外，我们还考虑了特殊情况，如爱因斯坦空间和Ricci零孤子。我们指出了这些空间在一些高维引力理论中的相关性。特别是，我们表明，里奇nilsolitons黎曼解决方案，某些高曲率引力理论。
英文摘要：
We discuss negatively curved homogeneous spaces admitting a simply transitive group of isometries, or equivalently, negatively curved left-invariant metrics on Lie groups. Negatively curved spaces have a remarkably rich and diverse structure and are interesting from both a mathematical and a physical perspective. As well as giving general criteria for having left-invariant metrics with negative Ricci curvature scalar, we also consider special cases, like Einstein spaces and Ricci nilsolitons. We point out the relevance these spaces play in some higher-dimensional theories of gravity. In particular, we show that the Ricci nilsolitons are Riemannian solutions to certain higher-curvature gravity theories.
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