SU上的左不变Grauert管（2）
Left-invariant Grauert tubes on SU(2)
摘要：
设M是实解析黎曼流形。TM上的适应复结构是零截面邻域上的复结构，使得黎曼叶理的叶是复子流形。如果这个结构可以扩展到整个TM，那么它就被称为整个TM。我们称这种流形为格劳尔特管，或简称为管。这里我们考虑M = G是一个具有左不变度量的紧致连通李群的情况，并试图确定对于哪些度量，相关的管是完整的。众所周知，李群上的双不变度量的Grauert管是整的。最小群SU（2）的情形得到了完全的处理，这要归功于这种度量的测地流的完全可积性，这是经典力学中的一个标准结果。一路上，我们发现了一个新的障碍，管是完整的，这是可见的完全可积性。(New参考和说明缩短，2017年11月17日。）
英文摘要：
Let M be a real analytic Riemannian manifold. An adapted complex structure on TM is a complex structure on a neighborhood of the zero section such that the leaves of the Riemann foliation are complex submanifolds. This structure is called entire if it may be extended to the whole of TM. We call such manifolds Grauert tubes, or simply tubes. We consider here the case of M = G a compact connected Lie group with a left-invariant metric, and try to determine for which such metrics the associated tube is entire. It is well-known that the Grauert tube of a bi-invariant metric on a Lie group is entire. The case of the smallest group SU(2) is treated completely, thanks to the complete integrability of the geodesic flow for such a metric, a standard result in classical mechanics. Along the way we find a new obstruction to tubes being entire which is made visible by the complete integrability. (New reference and exposition shortened, 11/17/2017.)
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