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arXiv · 1911.04003

The Spheres of Sol

Matei P. Coiculescu·Richard Evan Schwartz
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Abstract

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.

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Matei P. Coiculescu, Richard Evan Schwartz. 2019-11-10. The Spheres of Sol. https://doi.org/10.2140/gt.2022.26.2103

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