Isometries for the Caratheodory Metric

TL;DR

This paper proves that under certain conditions, a map preserving the Caratheodory infinitesimal metric at a point is necessarily an analytic isomorphism onto its image, highlighting a rigidity property of such isometries.

Contribution

It establishes a new rigidity result linking local isometries of the Caratheodory metric to global analytic isomorphisms under specific hypotheses.

Findings

Isometries for the Caratheodory metric are analytic isomorphisms under certain conditions.

The result extends understanding of the structure of Caratheodory metric isometries.

Provides conditions under which local isometries imply global analytic structure.

Abstract

Under certain hypothesises, we prove that a map which is an isometry for the Caratheodory infinitesimal metric at a point is an analytic isomorphism onto its image.