Teichm\"uller spaces and bounded symmetric domains do not mix isometrically

TL;DR

This paper proves that in dimensions two or higher, Teichmüller spaces and bounded symmetric domains cannot be isometrically equivalent under their intrinsic Kobayashi metrics.

Contribution

It establishes a non-existence result for holomorphic isometries between Teichmüller spaces and bounded symmetric domains in higher dimensions.

Findings

No holomorphic isometries exist between the spaces in dimensions two or more.

Teichmüller spaces and bounded symmetric domains are intrinsically distinct in their Kobayashi metrics.

The result applies to all higher-dimensional cases, confirming their geometric incompatibility.

Abstract

This paper shows that, in dimensions two or more, there are no holomorphic isometries between Teichm\"uller spaces and bounded symmetric domains in their intrinsic Kobayashi metrics.