The main result of this paper gives a new construction of extremal Kähler metrics on the total space of certain holomorphic submersions, giving a vast generalisation and unification of results of Hong, Fine and others. The principal new ingredient is a novel geometric partial differential equation on such fibrations, which we call the optimal symplectic connection equation.

中文翻译：

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全纯淹没的最优辛连接

本文的主要结果给出了关于某些全纯淹没总空间的极值 Kähler 度量的新构造，给出了 Hong、Fine 和其他人的结果的广泛概括和统一。主要的新成分是一种新的关于这种纤维化的几何偏微分方程，我们称之为最优辛连接方程。