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Gravitational instantons with faster than quadratic curvature decay (I)

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arxiv 1505.01790 v2 pith:WW4GT6JB submitted 2015-05-07 math.DG math-phmath.MP

Gao Chen , Xiuxiong Chen This is my paper · ORCID
classification math.DGmath-phmath.MP
keywords gravitationalmustcasescurvaturedecayfasterinstantonsquadratic
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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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  1. On the geometry of asymptotically flat manifolds

    math.DG 2019-08 conditional novelty 8.0 of 10

    Asymptotically flat manifolds with strong holonomy control are torus bundles over ALE ends, which yields Hitchin-Thorpe inequalities for Ricci-flat 4-manifolds and rigidity of Ricci-flat metrics on R^4.

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