Biholomorphism Rigidity for Transport Twistor Spaces

TL;DR

This paper establishes a rigidity result for biholomorphisms between transport twistor spaces of certain surfaces, showing they are essentially lifts of isometries, up to rescaling and antipodal maps.

Contribution

It proves a new rigidity theorem for biholomorphisms of transport twistor spaces associated with simple or Anosov surfaces, characterizing their structure.

Findings

Biholomorphisms are lifts of orientation-preserving isometries.

Such maps are unique up to rescaling and antipodal transformations.

The result applies specifically to simple or Anosov surfaces.

Abstract

We prove that biholomorphisms between the transport twistor spaces of simple or Anosov surfaces exhibit rigidity: they must be, up to constant rescaling and the antipodal map, the lift of an orientation preserving isometry.