The Covariance Metric in the Blaschke Locus

verfasst von: Xian Dai, Nikolas Eptaminitakis
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.
Organisationseinheit(en): Institut für Differentialgeometrie
Externe Organisation(en): Ruhr-Universität Bochum
Typ: Artikel
Journal: Journal of Geometric Analysis
Band: 34
Anzahl der Seiten: 54
ISSN: 1050-6926
Publikationsdatum: 05.2024
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Geometrie und Topologie
Elektronische Version(en): https://doi.org/10.48550/arXiv.2301.05289 (Zugang: Offen)
https://doi.org/10.1007/s12220-024-01586-w (Zugang: Offen)