Stable complex manifolds
Stable complex manifolds
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DOI：
10.1090/s0002-9904-1966-11610-5
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发表时间：
1966-11
影响因子：
1.3
通讯作者：
A. Brender
中科院分区：
文献类型：
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作者：
A. Brender
1. T.货车de Ven [3]最近证明了存在真实的4维流形，它们几乎允许复结构，但不允许复结构，例如SXS* # SXS # CP（2）.本说明的目的是说明这是一种不稳定的现象。设M是Cw维无边界真实的流形，TM是它的切丛. R是真实的欧氏fe-空间，C是复&-空间。定义1. M容许一个稳定的复结构，如果MXR可被给定为一个复解析流形的结构，其中k ^ 0，n = k（mod 2）。设ε是M上的m-平面丛。定义2.一个稳定的复结构是（··定义3. M的稳定的几乎复结构是TM的稳定复结构>
1. T. Van de Ven [3] has recently shown that there exist real 4dimensional manifolds which admit almost complex structures but admit no complex structures, e.g. SXS* # SXS # CP(2). The purpose of this note is to show that this is an unstable phenomenon. Let M be a C w-dimensional real manifold without boundary and let TM be its tangent bundle. R is real Euclidean fe-space and C is complex &-space. DEFINITION 1. M admits a stable complex structure if MXR can be given the structure of a complex analytic manifold for some k ^ 0, n = k (mod 2). Let £ be an m-plane bundle over M. DEFINITION 2. A stable complex structure for £ is a reduction of the group of (•»©€* to U((m+k)/2) for some feâO, m^k (mod 2). DEFINITION 3. A stable almost complex structure for M is a stable complex structure for TM>