权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Construction of pluriharmonic maps from complex torus into symmetric spaces and applications of the theory of integrable systems

从复环面到对称空间的多调和映射的构造及可积系统理论的应用

基本信息

批准号：
09640133
负责人：
UDAGAWA Seiichi
金额：
$ 0.96万
依托单位：
NIHON UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

项目摘要

In our study, I obtained three main results. I expain each of them separately.(1) F. Burstall proved that any weakly conformal non-isotropic harmonic map of 2-torus into a sphere or a complex projective space can be lifted to a primitive map of finite type into some k-symmetric space. We generalized the result of F. Burstall to obtain that any weakly conformal non-isotropic harmonic map of 2-torus into a sphere or a complex projective space is itself of finite type. In fact, we can prove a more general result. Given a primitive map of finite type into a generalized flag manifold, we can project it into some compact symmetric space as a harmonic map of finite type under some condition on the choice of isotropy subgroup of the compact symmetric space. The condition is rather mild and satisfied by the above cases (except odd-dimensional sphere. But, this case is included the case of even-dimensional sphere).(2) We extended the result (1) to the case where the domain is a complex manifold and pluriharmonic maps into it. We proved that any non-isotropic pluriharmonic map of complex torus into a complex projective space is of finite type.(3) We introduced the concept of primitive maps of generalized finite type and obtained some results on the harmonic maps of compact Riemann surfaces of higher genus. In fact, any primitive harmonic maps of generalized finite type of a compact Riemann surface of genus greater than 1 into a k-symmetric space is a composition of a primitive pluriharmonic map of finite type of some Jacobian torus into a k-symmetric space with a Abel map of the compact Riemann surface into the Jacobian torus.

在我们的研究中，我获得了三个主要的结果。我分别解释它们。(1) F. Burstall证明了任何2环面的弱共形非各向同性调和映射到球面或复射光空间中，都可以提升到k对称空间的有限型原始映射。推广了F. Burstall的结果，得到了2-环面的任何弱共形非各向同性调和映射到球面或复射影空间本身都是有限型的。事实上，我们可以证明一个更一般的结果。给定一个有限型原始映射到广义标志流形上，在紧致对称空间各向同性子群选择的一定条件下，我们可以将其作为有限型调和映射投影到紧致对称空间上。上述情形（奇维球面除外）的条件都是相当温和的。但是，这种情况包括了偶维球的情况。(2)将结果(1)推广到域是复流形且多谐映射到其中的情况。证明了复环面到复射影空间的任何非各向同性多谐映射都是有限型的。(3)引入了广义有限型原始映射的概念，得到了高格紧致Riemann曲面调和映射的一些结果。事实上，在k对称空间中，任何属大于1的紧致黎曼曲面的广义有限型原始调和映射都是某个雅可比环面的有限型原始多调和映射与紧致黎曼曲面的雅可比环面的阿贝尔映射的复合。