比二次曲率衰减更快的引力瞬子。我

IF 4.9 1区数学 Q1 MATHEMATICS

Acta Mathematica Pub Date : 2022-01-10 DOI:10.4310/acta.2021.v227.n2.a2

Gao Chen, Xiuxiong Chen

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引用次数: 7

摘要

在本文中，我们研究了引力瞬子(即，比二次曲率衰减更快的完全hyperkähler $4$ -流形)。我们证明了三个主要定理:(1)任何引力瞬子必须有以下已知端点之一:ALE, ALF, ALG和ALH。(2)在ALG和ALH非分裂情况下，它必须是生物全纯的紧复椭圆曲面减去一个除数。因此，我们在ALG和ALH病例中确认了一个长期存在的问题。(3)在ALF - $D_k$的情况下，它必须有一个$O(4)$ - multiplet。

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Gravitational instantons with faster than quadratic curvature decay. I

In this paper, we study gravitational instantons (i.e., complete hyperkähler $4$‑manifolds with faster than quadratic curvature decay). We prove three main theorems: (1) Any gravitational instanton must have one of the following known ends: ALE, ALF, ALG, and ALH. (2) In the ALG and ALH non-splitting cases, it must be biholomorphic to a compact complex elliptic surface minus a divisor. Thus, we confirm a long-standing question of Yau in the ALG and ALH cases. (3) In the ALF‑$D_k$ case, it must have an $O(4)$‑multiplet.

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来源期刊

Acta Mathematica 数学-数学

CiteScore

6.00

自引率

2.70%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes original research papers of the highest quality in all fields of mathematics.