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Gravitational instantons with faster than quadratic curvature decay (I). (arXiv:1505.01790v2 [math.DG] UPDATED)
来源于:arXiv
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. 查看全文>>