Characteristic forms of complex Cartan geometries III: G-structures

TL;DR

This paper explores characteristic class relations in complex Cartan geometries, demonstrating how they can be derived from representation theory without metric dependence, and extends previous work to include infinite type structures.

Contribution

It advances the theory of complex Cartan geometries by generalizing characteristic class calculations to infinite type structures, bypassing metric and cohomology group dependencies.

Findings

Characteristic class relations derived from representation theory.

Extension to infinite type geometric structures.

Simplified calculation method without metric or cohomology knowledge.

Abstract

Characteristic class relations in Dolbeault cohomology follow from the existence of a holomorphic geometric structure (for example, holomorphic conformal structures, holomorphic Engel distributions, holomorphic projective connections, and holomorphic foliations). These relations can be calculated directly from the representation theory of the structure group, without selecting any metric or connection or having any knowledge of the Dolbeault cohomology groups of the manifold. This paper improves on its predecessor [17] by allowing infinite type geometric structures.