Gravitational instantons with faster than quadratic curvature decay. I
Gao Chen, Xiuxiong Chen
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.
Topics & Concepts
InstantonCurvatureRiemann curvature tensorPhysicsGravitationMultipletQuadratic equationMathematical physicsDivisor (algebraic geometry)MathematicsPure mathematicsGeometryClassical mechanicsQuantum mechanicsSpectral lineGeometric and Algebraic TopologyGeometric Analysis and Curvature FlowsGeometry and complex manifolds