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arXiv · 1505.01790

Gravitational instantons with faster than quadratic curvature decay (I)

Gao Chen·Xiuxiong Chen
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Abstract

In this paper, we study gravitational instantons (i.e., complete hyperk\"aler 4-manifolds with faster than quadratic curvature decay). We prove three main theorems: 1.Any gravitational instanton must have known end----ALE, ALF, ALG or ALH. 2.In 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 ALG and ALH cases. 3.In ALF-D_k case, it must have an O(4)-multiplet.

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BibTeXRIS

Gao Chen, Xiuxiong Chen. 2015-05-07. Gravitational instantons with faster than quadratic curvature decay (I). https://doi.org/10.4310/acta.2021.v227.n2.a2

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