From Hypercomplex to Holomorphic Symplectic Structures

TL;DR

This paper introduces and proves the equivalence of holomorphic symplectic and hypercomplex structures on Courant algebroids, generalizing classical geometric structures on manifolds.

Contribution

It establishes the equivalence between holomorphic symplectic and hypercomplex structures on Courant algebroids, extending known geometric concepts.

Findings

Holomorphic symplectic and hypercomplex structures are equivalent on Courant algebroids.

Basic properties of these structures are systematically established.

The work generalizes classical structures from manifolds to Courant algebroids.

Abstract

The notions of holomorphic symplectic structures and hypercomplex structures on Courant algebroids are introduced and then proved to be equivalent. These generalize hypercomplex triples and holomorphic symplectic 2-forms on manifolds respectively. Basic properties of such structures are established.