On holomorphic maps and Generalized Complex Geometry

TL;DR

This paper introduces a new concept of holomorphic maps between generalized complex manifolds and explores their properties in relation to Dirac structures and generalized Kähler geometry.

Contribution

It defines a natural notion of holomorphic maps in the context of generalized complex geometry and establishes foundational results linking these maps to Dirac structures.

Findings

Established a definition of holomorphic maps for generalized complex manifolds.

Proved results connecting these maps to Dirac structures.

Explored implications for generalized Kähler manifolds.

Abstract

We introduce a natural notion of holomorphic map between generalized complex manifolds and we prove some related results on Dirac structures and generalized Kaehler manifolds.