Families of equivariant immersions in $H^3$ with holomorphic holonomy

Abstract: Given an equivariant immersion of a surface in the hyperbolic 3-space, a typical problem consists in understanding whether a deformation of the immersion (parametrized over a complex manifold) produces a holomorphic deformation of its mondromy in PSL(2,C). In this talk we present a simple “trick” providing a sufficient condition for this property, offering for instance an alternative proof of the holomorphicity of the complex landslide flow. This result is a consequence of the study of immersions into the space of geodesics of the hyperbolic 3-space, seen as a holomorphic Riemannian manifold, whose key features will be discussed in the talk.

This is joint work with Francesco Bonsante

differential geometry

Audience: researchers in the topic

Pangolin seminar

Series comments: TIME HAS CHANGED: 15:30 Paris 10:30AM Rio de Janeiro

Description: Differential geometry seminar

Zoom link posted on the webpage 15 minutes before each lecture: https://sites.google.com/view/pangolin-seminar/home