Mirror symmetry conjecture over open Calabi-Yau's with boundaries

有边界的开放卡拉比-丘的镜像对称猜想

• 批准号: 16540077
• 负责人: AKAHORI Takao
• 金额: $ 0.51万
• 依托单位: University of Hyogo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540077/
• 关键词: CR structure; isolated sing; pseudo convex; CR幾何; 弦理論; CR幾何学

The purpose of this research is to study the CR geometry and apply for string theory.Kapustin and Orlov introduce the notion A brane, which is a special type of D branes. Let W be a Kaehler manifold.A brane consists of a submanifold of this W and line bundle with connection, which satisfies additional condition.Inspired by the Kapustin-Orlov's work, the author constructs deformation theory of A branes, and study the relation with Hamiltonian mechanics of this submanifold. This work is still in progress and a part of my work appears in JMAA, N.322(2006), p207-p213. And especially, the new notion of CR Hamiltonian flow leads to a recent work of Einstein metric on CR manifolds.

本研究的目的是研究CR几何并应用于弦理论。Kapustin和Orlov引入了A膜的概念，它是D膜的一种特殊类型。设W为凯勒流形。膜由该W的子流形与满足附加条件的线丛组成。受Kapustin-Orlov工作的启发，作者构建了A膜的变形理论，并研究了与哈密顿量的关系该子流形的力学。这项工作仍在进行中，我的部分工作出现在 JMAA, N.322(2006), p207-p213 中。特别是，CR 哈密顿流的新概念催生了爱因斯坦度量在 CR 流形上的最新工作。

项目成果

The canonical Kaehler potential on the parameter space of the versal family of CR structures

CR结构通用族参数空间上的规范凯勒势

• 发表时间: 2004
• 期刊: J.Math.Anal.Appl. 300
• 作者: Nakao Kamada;Yasuyuki Miyazawa;Y.Hemmi;M.Furushima;Takao AKAHORI
• 通讯作者: Takao AKAHORI

The Hamiltonian dynamics over real hypersurfaces in Kaehler manifolds

凯勒流形中真实超曲面上的哈密顿动力学

• 发表时间: 2006
• 期刊: Journal of Mathematical Analysis and Application 322
• 作者: S.Yamamoto;M.Fukuda;井上光輝;加藤武紀;T.Kawaguchi;Takao Akahori
• 通讯作者: Takao Akahori