HARMONIC MAPS INTO SYMMETRIC SPACES AND GEOMETRY OF MODULI SPACES

调和映射到对称空间和模空间的几何

基本信息

批准号：
11640088
负责人：
OHNITA Yoshihiro
金额：
$ 2.3万
依托单位：
Tokyo Metropolitan University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640088/
关键词：
Harmonic map Symmetric space Moduli space Yang-Mills-Higgs equation Integrable system

项目摘要

Harmonic maps into symmetric spaces have several characteristic properties that harmonic maps into general Riemannian manifolds do not have. For example such harmonic map equation can be formulated as the zero curvature equation, the Lax equation and gauge-theoretic equations. As an approach for harmonic maps into symmeric spaces, we investigate the gauge-theoretic equations associated to such harmonic maps and the structure and the geometry of the moduli spaces of their solutions, and we obatined several results. I have written up the paper entitled with "Geoemtry of the moduli spaces of harmonic maps into Lie groups via gauge theory over Riemann surfaces" This work was estimated by foreign researchers as it is very interesting and imformative. Furthermore, we studied harmonic maps of finite type which is a class of harmonic maps into compact symmetric spaces. We introduced the notion of harmonic maps of generalized finite type from compact Riemann surfaces to compact k-symmetric spac … More es, and we proved that such a harmonic map is the composition of the Abel map from a compact Riemann surface to the Jacobi variety and a pluriharmonic map from the Jacobi variety to a k-symmetric space. We have written up the paper entitled with "Harmonic maps of finite type into generalized flag manifolds and twistor fibrations" They will be published in Inter. J. Math. And J. London Math. Soc., respectively. On the other hand, as the research related to integrable systems, we give our attention to the relationship between Frobenius manifolds and pluriharmonic maps. It is now in progress to study Hamiltonian stability problem for compact minimal Lagrangian submanifolds in complex projective spaces and Hermitian symmetric spaces constructed by using the symmetric space theory and we obtain new results on it.The collaborator, Makiko Tanaka, treated symmetric R-spaces with nice properties in symmetric spaces and gave the new characterization of symmetric R-spaces from the viewpoint of the basic theory in the category of symmetric spaces through stays at Max-Planck-Institut fuer Mathematik in Bonn, Germany etc. The collaborator, Masatoshi Kokubu,showed new results on propeties and construction of complete isotropic minimal surfaces in odd-dimensional Euclidean space. The collaborator, Hideko Hashiguchi, gave a research report on problems about moduli space of unitons corresponding to harmonic maps from a Riemann sphere into the unitary group at this research meeting. Less

谐波图中的对称空间具有几种特征性能，可谐波地图成一般的riemannian歧管。例如，此类谐波映射到零曲率方程，宽松方程和规格理论方程。作为谐波映射到符号空间的方法，我们研究了与此类谐波图以及其解决方案模量空间的结构和几何形状相关的量规理论方程，并遵守了几个结果。我已经写了题为“谐波图的模态空间的地理学空间，通过仪表理论通过riemann表面进行谎言组”，这项工作是由外国研究人员估算的，因为它非常有趣且具有丰富的信息。此外，我们研究了有限类型的谐波图，这是一类谐波图，分为紧凑的对称空间。我们介绍了从紧凑的Riemann表面的广义有限类型的谐波图的概念，以紧凑的K-对称空间……更多的ES，我们证明了这样的谐波图是从紧凑型Riemann Surface到Jacobi品种的ABEL地图的组成，从Jacobi品种和来自Jacobi品种的Pluriharmonic Map到jacobi valters to k-sym-emptrics k-sympremmetmemmetmemmetmemmetmemmets。我们已经写了题为“有限类型的谐波图成为通用的标志歧管和曲折纤维”的论文。 J. Math。和J.伦敦数学。另一方面，作为与整合系统有关的研究，我们关注了Frobenius歧管和Pluriharmonic地图之间的关系。现在正在进行研究哈密顿的稳定性问题，用于复杂的投影空间中的紧凑型拉格朗日式亚曼福尔德和通过使用对称空间理论所构建的赫米利亚对称空间，并在其上获得新的结果。通过在德国波恩的Max-Planck-Institut Fuer Mathematik暂停的对称空间。合作者Hideko Hashiguchi在这次研究会议上提供了有关与Riemann Sphere相对应的统一地图的统一地图的模量空间的研究报告。较少的