The spheres of Sol
The spheres of Sol
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太阳系球体
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
R. Schwartz
中科院分区：
文献类型：
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作者：
Matei P. Coiculescu;R. Schwartz
设Sol为具有标准左不变黎曼度规的三维可解李群。在黎曼指数映射为微分同构的李代数中，我们给出了单位的切轨迹的精确描述，以及黎曼指数映射的极大定义域。因此，我们证明了Sol中的度规球是拓扑球，并几乎准确地描述了它们的奇点。
Let Sol be the three-dimensional solvable Lie group equipped with its standard left-invariant Riemannian metric. We give a precise description of the cut locus of the identity, and a maximal domain in the Lie algebra on which the Riemannian exponential map is a diffeomorphism. As a consequence, we prove that the metric spheres in Sol are topological spheres, and we characterize their singular points almost exactly.