A differential-geometric analysis of the Bergman representative map

TL;DR

This paper explores the relationship between the exponential map of the Bochner connection and Bergman's representative map on complex manifolds with positive-definite Bergman metrics, providing new insights and generalizations.

Contribution

It establishes that the exponential map of the Bochner connection is the inverse of Bergman's representative map and generalizes the Lu theorem.

Findings

Exponential map coincides with the inverse of Bergman's representative map.

Provides a generalized version of the Lu theorem.

Enhances understanding of the geometric structure of complex manifolds with Bergman metrics.

Abstract

We show that the exponential map of the Bochner connection on the restricted holomorphic tangent bundle of a complex manifold admitting the positive-definite Bergman metric coincides with the inverse of Bergman's representative map. We also present a generalization of the Lu theorem, as an application.