Homogeneous spaces and variational problems

齐次空间和变分问题

• 批准号: 14540058
• 负责人: TASAKI Hiroyuki
• 金额: $ 2.37万
• 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: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540058/
• 关键词: homogeneous spaces; variational problems; integral geometry; 交叉積分公式; Poincareの公式; Croftonの公式; Kahler角度

The head investigator introduced the notion "multiple Kahler angle" and showed that we can describe integral geometry of submanifolds in complex projective spaces explicitly by the use of multiple Kahler angle. In the case of the complex projective plane he obtained with Kang more detailed Poincare formula. These Poincare formulae has an application on estimate of the area and the integral of Kahler angle of real surfaces. By this estimate we can get a minimizing solution of a certain variational problem. Moreover the head investigator published Poincare formula of real surfaces and submanifolds of codimension 2. The calculation of this result is obtained by the use of an integral on a Lie group and some symmetric pairsThe head investigator showed that an integral on a Lie group by the use of some symmetric pairs is effective in formulation of Poincare formulae in the other homogeneous spaces. Takahashi, Kang, Sakai and the head investigator has studied integral geometry of almost complex submanifolds in homogeneous almost Hermitian spaces and formulated Poincare formulae of almost complex submanifolds in homogeneous almost Hermitian spaces, which are generalization of classical and fundamental formulae in complex projective spaces obtaind by Santalo. Sakai has generalized these results

首席研究员介绍了“多个Kahler角”概念，并表明我们可以通过使用多个Kahler角度明确地描述复杂射击空间中亚体的积分几何形状。在使用Kang更详细的Poincare公式获得的复杂投影平面的情况下。这些繁殖性公式在估计区域的估计值和实际表面的Kahler角度的估计值上进行了应用。通过此估计，我们可以最大程度地减少某个变异问题的解决方案。此外，首席调查员发表了真实表面和Codimension 2的庞康奶油公式。某些对称对有效地在其他同质空间中制定了繁殖公式。高桥，康，Sakai和首席调查员研究了几乎复杂的次级体的整体几何形状，几乎是均质的几乎是遗产空间中的几乎是复杂的，并在几乎同质性的遗传空间中制定了几乎复杂的submanifolds的庞加利公式，这是复杂项目中经典和基本形式的普遍性的均匀遗传学空间。圣塔洛。 Sakai概括了这些结果

项目成果

M.Itoh: "Contact metric 5-manifolds, CR twistor spaces and integrability"Jour. Math. Phys.. 43・7. 3783-3797 (2002)

M.Itoh：“接触度量 5 流形、CR 扭转空间和可积性”数学杂志 43・7（2002）。

H.Tasaki: "Generalization of Kahler angle and integral geometry in complex projective spaces II"Math.Nachr.. 252. 106-112 (2003)

H.Tasaki：“复射影空间中卡勒角和积分几何的推广 II”Math.Nachr.. 252. 106-112 (2003)

H.Tasaki: "Integral geometry under the action of the first symplectic group"Archiv der Mathematik (Basel). 80. 106-112 (2003)

H.Tasaki：“第一辛群作用下的积分几何”Archiv der Mathematik（巴塞尔）。

O.Ikawa: "Hamiltonian dynamics of a charged particle"Hokkaido Math.J.. 32・3. 661-671 (2003)

大井川：“带电粒子的哈密尔顿动力学”Hokkaido Math.J. 32・3（2003）

H.Tasaki, Kang: "Integral geometry of real surfaces in the complex projective plane"Geometriae Dedicata. 90. 99-106 (2002)

H.Tasaki, Kang：“复射影平面中真实表面的积分几何”Geometriae Dedicata。