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

Metric Reduction and Generalized Holomorphic Structures