Collapsing geometry of hyperk"ahler 4-manifolds and applications
Collapsing geometry of hyperk"ahler 4-manifolds and applications
复制标题
hyperk"ahler 4-流形的折叠几何及其应用
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Ruobing Zhang
中科院分区：
文献类型：
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作者：
Song Sun;Ruobing Zhang
研究了hyperk "ahler四维流形的坍缩几何。作为应用，我们证明了该领域的两个著名的定理。(1)K3流形上单位直径超k "ahler度量的任何塌缩极限都等距于以下之一：平坦3-环面与对合的商，2-球面上的奇异特殊K" ahler度量，或单位区间。(2)任何具有有限能量的完备hyperk "ahler 4-流形（即，引力瞬子）在无穷远处是渐近的。
We investigate the collapsing geometry of hyperk"ahler 4-manifolds. As applications we prove two well-known conjectures in the field. (1) Any collapsed limit of unit-diameter hyperk"ahler metrics on the K3 manifold is isometric to one of the following: the quotient of a flat 3-torus by an involution, a singular special K"ahler metric on the 2-sphere, or the unit interval. (2) Any complete hyperk"ahler 4-manifold with finite energy (i.e., gravitational instanton) is asymptotic to a model end at infinity.