Gravitational instantons with faster than quadratic curvature decay (I)
Differential Geometry
2022-01-17 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1505.01790,
title = {Gravitational instantons with faster than quadratic curvature decay (I)},
author = {Gao Chen and Xiuxiong Chen},
journal= {arXiv preprint arXiv:1505.01790},
year = {2022}
}