Homogeneous spaces and variational problems

齐次空间和变分问题

• 批准号: 12640058
• 负责人: TASAKI Hiroyuki
• 金额: $ 2.24万
• 依托单位: University of Tsukuba
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640058/
• 关键词: homogeneous space; symmetric space; variational problem; integral geometry; Kahler angle; 極小曲面

The head investigator has developed explicit expressions of Poincare integral formulas in order to apply these formulas of integral geometry to variational problems in homogeneous spaces. He has obtained an explicit representa tion of Poincare formula of real surfaces in the complex projective spaces in terms of the Kahler angles of those surfaces. This is the first explicit one in which the integral of intersection numbers is not expressed by the product of the volumes of submanifolds. After this in order to generalize this formula to those for general real submanifolds in the complex projective spaces he defined multiple Kahler angles which were generalizations of Kahler angle. According to the multiple Kahler angle he has developed Poincare formulas of general real submanifolds in the complex projective spaces. As a conse quence a relation among some integrals of the multiple Kahler angles and the volumes of submanifolds can be obtained and will become a tool for variational problems.

首席研究员已经开发了庞加雷积分公式的明确表达式，以便将这些积分几何形状的公式应用于均匀空间中的各种问题。就这些表面的卡勒角角（Kahler Ancles）而言，他已经明确表示了复杂的投影空间中真实表面的繁殖性公式。这是第一个显式的，其中相交数的积分不是由子手机体积的乘积表达的。之后，为了将这个公式概括为复杂的射影空间中的一般真实子曼群的公式，他定义了多个卡勒角，这是卡勒角的概括。根据多个Kahler角度，他在复杂的投影空间中开发了一般真实子手机的庞加罗公式。作为conse态度，可以获得多个卡勒角的某些积分之间的关​​系和子曼群的体积，并将成为变异问题的工具。

项目成果

D.Hirohashi, H.Song, R.Takagi, H.Tasaki: "Minimal orbits of the isotropy groups of symmetric spaces of compact type"Diferential Geometry Appl.. 13. 167-177 (2000)

D.Hirohashi、H.Song、R.Takagi、H.Tasaki：“紧型对称空间各向同性群的最小轨道”微分几何应用.. 13. 167-177 (2000)

H. Kaji, O. Yasukura: "Tangent loci and certain linear sections of adjoint varieties"Nagoya Math. J.. 158. 63-72 (2000)

H. Kaji，O. Yasukura：“伴随变体的切线轨迹和某些线性部分”名古屋数学。

H.Tasaki: "Generalization of Kahler angle and integral geometry in complex projective spaces"Steps in Differential Geometry. 349-361 (2001)

H.Tasaki：“复杂射影空间中卡勒角和积分几何的推广”微分几何的步骤。

R. Aiyama, K. Akutagawa: "Kenmotsu type representation formula, for surfaces with prescribed mean curvature in the hyperbolic 3-space"J. Math. Soc. Japan. 52. 877-898 (2000)

R. Aiyama，K. Akutakawa：“Kenmotsu 型表示公式，用于双曲 3 空间中具有规定平均曲率的表面”J。

Y. Nagatomo: "Dimensional reduction and momentum maps"J. Geometry and Physics. 41. 208-223 (2002)

Y. Nagatomo：“降维和动量图”J。