The covariance metric in the Blaschke locus
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917660214689792 |
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| author | Dai, Xian Eptaminitakis, Nikolas |
| author_facet | Dai, Xian Eptaminitakis, Nikolas |
| contents | We prove that the Blaschke locus has the structure of a finite dimensional smooth manifold away from the Teichm{ü}ller space and study its Riemannian manifold structure with respect to the covariance metric introduced by Guillarmou, Knieper and Lefeuvre in \cite{GeodesicStretch}. We also identify some families of geodesics in the Blaschke locus arising from Hitchin representations for orbifolds and show that they have infinite length with respect to the covariance metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_05289 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The covariance metric in the Blaschke locus Dai, Xian Eptaminitakis, Nikolas Differential Geometry Geometric Topology We prove that the Blaschke locus has the structure of a finite dimensional smooth manifold away from the Teichm{ü}ller space and study its Riemannian manifold structure with respect to the covariance metric introduced by Guillarmou, Knieper and Lefeuvre in \cite{GeodesicStretch}. We also identify some families of geodesics in the Blaschke locus arising from Hitchin representations for orbifolds and show that they have infinite length with respect to the covariance metric. |
| title | The covariance metric in the Blaschke locus |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2301.05289 |