Kähler Metrics on Toric Orbifolds
Kähler Metrics on Toric Orbifolds
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Toric Orbifold 的 Kähler 指标
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
M. Abreu
中科院分区：
文献类型：
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作者：
M. Abreu
E. Lerman和S. Tolman的一个定理，推广了T. Delzant的结果，指出紧辛环轨道是由它们的矩多面体分类的，它们的每一个面都有一个正整数标记。本文利用这一结果和“全局”作用角坐标的存在性，利用相应矩多面体上的光滑函数，给出了紧辛环面上所有相容环面复结构的有效参数化。这等价于所有环面Kahler度量的参数化，并推广了环面流形的类似结果。一个简单的显式描述的有趣的家族的极值Kahler度量，由R. Bryant最近的工作，给出了一个应用的方法在本文中。在四维中，这些度量是自对偶和共形爱因斯坦的事实也被讨论。这特别产生了一个单参数的自对偶爱因斯坦度量族，连接着众所周知的Eguchi-Hanson和Taub-NUT度量。
A theorem of E. Lerman and S. Tolman, generalizing a result of T. Delzant, states that compact symplectic toric orbifolds are classified by their moment polytopes, together with a positive integer label attached to each of their facets. In this paper we use this result, and the existence of “global” action-angle coordinates, to give an effective parametrization of all compatible toric complex structures on a compact symplectic toric orbifold, by means of smooth functions on the corresponding moment polytope. This is equivalent to parametrizing all toric Kahler metrics and generalizes an analogous result for toric manifolds. A simple explicit description of interesting families of extremal Kahler metrics, arising from recent work of R. Bryant, is given as an application of the approach in this paper. The fact that in dimension four these metrics are selfdual and conformally Einstein is also discussed. This gives rise in particular to a one parameter family of self-dual Einstein metrics connecting the well known Eguchi-Hanson and Taub-NUT metrics.