Details
| Original language | English |
|---|---|
| Article number | 145 |
| Number of pages | 54 |
| Journal | Journal of Geometric Analysis |
| Volume | 34 |
| Issue number | 5 |
| Early online date | 25 Mar 2024 |
| Publication status | Published - May 2024 |
Abstract
We prove that the Blaschke locus has the structure of a finite dimensional smooth manifold away from the Teichmüller space and study its Riemannian manifold structure with respect to the covariance metric introduced by Guillarmou, Knieper and Lefeuvre in Guillarmou et al. in (Ergod Theory Dyn Syst 43:974–1022, 2021). 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.
Keywords
- 53C21, 58J05, Blaschke locus, Covariance metric, Hitchin representations
ASJC Scopus subject areas
- Mathematics(all)
- Geometry and Topology
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In: Journal of Geometric Analysis, Vol. 34, No. 5, 145, 05.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The Covariance Metric in the Blaschke Locus
AU - Dai, Xian
AU - Eptaminitakis, Nikolas
N1 - Funding Information: Open Access funding enabled and organized by Projekt DEAL.
PY - 2024/5
Y1 - 2024/5
N2 - We prove that the Blaschke locus has the structure of a finite dimensional smooth manifold away from the Teichmüller space and study its Riemannian manifold structure with respect to the covariance metric introduced by Guillarmou, Knieper and Lefeuvre in Guillarmou et al. in (Ergod Theory Dyn Syst 43:974–1022, 2021). 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.
AB - We prove that the Blaschke locus has the structure of a finite dimensional smooth manifold away from the Teichmüller space and study its Riemannian manifold structure with respect to the covariance metric introduced by Guillarmou, Knieper and Lefeuvre in Guillarmou et al. in (Ergod Theory Dyn Syst 43:974–1022, 2021). 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.
KW - 53C21
KW - 58J05
KW - Blaschke locus
KW - Covariance metric
KW - Hitchin representations
UR - http://www.scopus.com/inward/record.url?scp=85188621875&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2301.05289
DO - 10.48550/arXiv.2301.05289
M3 - Article
AN - SCOPUS:85188621875
VL - 34
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
SN - 1050-6926
IS - 5
M1 - 145
ER -