Geometry of Selberg's bisectors in the symmetric space $SL(n,\mathbb{R})/SO(n,\mathbb{R})$
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909421503774720 |
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| author | Du, Yukun |
| author_facet | Du, Yukun |
| contents | We discussed some properties of a family of symmetric spaces, namely $\mathcal{P}(n):=SL(n,\mathbb{R})/SO(n,\mathbb{R})$, where we replace the Riemannian metric on $\mathcal{P}(n)$ with a premetric suggested by Selberg. These properties are generalizations of properties on the hyperbolic spaces $\mathbf{H}^n$ related to Poincaré's fundamental polyhedron theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_00643 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Geometry of Selberg's bisectors in the symmetric space $SL(n,\mathbb{R})/SO(n,\mathbb{R})$ Du, Yukun Group Theory Differential Geometry 20F65 (Primary) 22E40, 53C35 (Secondary) We discussed some properties of a family of symmetric spaces, namely $\mathcal{P}(n):=SL(n,\mathbb{R})/SO(n,\mathbb{R})$, where we replace the Riemannian metric on $\mathcal{P}(n)$ with a premetric suggested by Selberg. These properties are generalizations of properties on the hyperbolic spaces $\mathbf{H}^n$ related to Poincaré's fundamental polyhedron theorem. |
| title | Geometry of Selberg's bisectors in the symmetric space $SL(n,\mathbb{R})/SO(n,\mathbb{R})$ |
| topic | Group Theory Differential Geometry 20F65 (Primary) 22E40, 53C35 (Secondary) |
| url | https://arxiv.org/abs/2302.00643 |