The existence of anti-self-dual conformal structures
The existence of anti-self-dual conformal structures
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反自对偶共形结构的存在
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发表时间：
1992
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通讯作者：
C. Taubes
中科院分区：
文献类型：
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作者：
C. Taubes
在这里，s是通常的标态曲率，b是无纹状体张量（在不寻常的吉他中），而w±分别是自助式和抗ful-seftul-seftul-seftul-fel-seftul-fluctual tensric（指标是Einstein。 ，如果W+和2γ均为零。讨论W+ -0。我们给出了主要结果：定理1表示所有足够大的n，m＃n£p 2的操作。 X中的球在y中，然后识别两个结果的边界3秒。
Here, s is the usual scalar curvature, B is the traceless Ricci tensor (in an unusual guise), and the W± are, respectively, the self-dual and anti-selfdual Weyl tensors. (The metric is Einstein if B — 0, and it is conformally flat if W+ and 2Γ. are both zero.) (a) Existence. Given that this preamble is understood (and [1] is the canonical reference), it can be said that the purpose of this article is to discuss metrics with W+ — 0. We give the main result: Theorem 1.1. Let M be a smooth, compact, oriented, 4-dimensional manifold. Use CP to denote complex projective 2-space with the opposite of its complex orientation. Use # to denote the operation of connect sum. For all sufficiently large N, MN = M#N£P 2 admits a metric with W+=0. Remark that the connect sum of manifolds X and Y is obtained from their disjoint union by cutting out an open ball in X and one in Y and then identifying the two resulting boundary 3-spheres.