Rigidity of a family of spherical conical metrics

Abstract

We study the deformation of spherical conical metrics with at least some of the cone angles larger than $2\pi$. We show in this note via synthetic geometry that for one family of such metrics, there is local rigidity in the choice of cone positions if angles are fixed. This gives an evidence of the analytic obstruction considered in recent works of Mazzeo and author.

14 pages, 7 figures

References in corpus (2)

• Conical metrics on Riemann surfaces, II: spherical metrics
• Spherical metrics with conical singularities on 2-spheres

Cited by in corpus (3)

• Conical metrics on Riemann surfaces, II: spherical metrics
• Irreducible cone spherical metrics and stable extensions of two line bundles
• Cone spherical metrics and stable vector bundles