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arXiv · 2301.05289

The covariance metric in the Blaschke locus

Xian Dai·Nikolas Eptaminitakis
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Abstract

We prove that the Blaschke locus has the structure of a finite dimensional smooth manifold away from the Teichm{\"u}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.

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Xian Dai, Nikolas Eptaminitakis. 2023-01-12. The covariance metric in the Blaschke locus. https://arxiv.org/abs/2301.05289

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