Metric Reduction and Generalized Holomorphic Structures

TL;DR

This paper explores metric reduction in generalized geometry, deriving Bismut connections on quotients, and introduces generalized holomorphic line bundles over complex projective space with non-trivial structures.

Contribution

It provides a method to obtain Bismut connections on quotient manifolds and constructs new generalized holomorphic line bundles with complex structures.

Findings

Derived Bismut connections on quotient manifolds.

Constructed a family of generalized holomorphic line bundles.

Analyzed generalized Kähler reduction processes.

Abstract

In this paper, metric reduction in generalized geometry is investigated. We show how the Bismut connections on the quotient manifold are obtained from those on the original manifold. The result facilitates the analysis of generalized K$\ddot{a}$hler reduction, which motivates the concept of metric generalized principal bundles and our approach to construct a family of generalized holomorphic line bundles over $\mathbb{C}P^2$ equipped with some non-trivial generalized K$\ddot{a}$hler structures.