The covariance metric in the Blaschke locus

Abstract

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.

Final version. Accepted by the Journal of Geometric Analysis