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Grauert Tubes over Non-compact Manifolds

发布者:澳门新葡8455最新网站   发布时间:2018-07-15  浏览次数:128



系列学术活动之(43

题    目:

Grauert Tubes over Non-compact Manifolds

摘    要:

It is well-known that a real analytic manifold X admits a complexificationXC, a complex manifold that contains X as the fixed point set of an antiholomorphic involution. This can be seen as follows. The transition functionsdefining the manifold X are real analytic local diffeomorphisms of Rn. The Taylor expansions of these transition functions can be considered as localbiholomorphisms of Cn, hence they serve as transition functions of a complexmanifold. The germ of the complexification XC is unique.In general the complex structure on the tubular neighborhood is not uniquesince there are many ways to embed it into XC. There have been a lot ofinterest in finding canonical complex structures on tubular neighborhoods ofX in T XWe discuss rigidity of Grauert Tubes.

Theorem (Kan and Ma)Let X be a compact Riemannian manifold of constant curvature. Then each Grauert tube of finite radius over X has a uniquecenter. Theorem (Kan and Ma)Let X be a locally symmetric Riemannian manifold. Then each Grauert tube of radius less than maximal over X has a uniquecenter

报 告 人:

马道玮,教授,威奇托州立大学

时    间:

201871616:30-17:30

地    点:

科技大楼605

 报告人概况:

 马道玮,美国威奇托州立大学(Wichita State University)数学与统计系教授, 博士生导师。北京大学本科毕业,获得武汉大学和Washington University in St. Louis双博士学位。在复分析与复几何领域做出了大量重要的工作,在包括 《Duke Mathematical Journal, Mathematische Annalen, American Journal of Mathematics,Communications in Partial Differential Equations,Journal fur die reine und angewandte mathematic》,《Mathematische Zeitschrift 》等著名数学期刊发表了约50篇论文。







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