Metric Reduction and Generalized Holomorphic Structures

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.

arXiv commentpresentation improved

References in corpus (9)

• Reduction of Courant algebroids and generalized complex structures
• Generalized complex geometry
• Instantons, Poisson structures and generalized Kaehler geometry
• Balanced Topological Field Theories
• Symmetries in generalized Kähler geometry
• Generalized Kaehler geometry of instanton moduli spaces
• The GIT aspect of generalized K$\ddot{a}$hler reduction. I
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Cited by in corpus (3)

• The GIT aspect of generalized K$\ddot{a}$hler reduction. I
• Toric generalized Kaehler structures. III
• Metric Reduction in Generalized Geometry and Balanced Topological Field Theories