Integral geometry in homogeneous spaces and its applications

均匀空间中的积分几何及其应用

• 批准号: 18540065
• 负责人: TASAKI Hiroyuki
• 金额: $ 2.5万
• 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: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540065/
• 关键词: weakly reflective orbit; austere orbit; Riemannian symmetric pair; kinematic formula; multiple Kaehler angle; integral geometry; Riemann等質空間; Riemann対称空間; Croftonの公式; 鏡映部分多様体; 弱鏡映部分多様体; austere部分多様体

In the research of integral geometry in the homogeneous space, integration on the orbit of a linear isotoropy action performs the key role. Many of important examples are austere submanifolds. The representative, Ikawa and Sakai classified the austere orbits of linear isotoropy actions of the Riemann symmetry pair in the sphere. When those austere orbits were examined in detail, a lot of austere orbits have not only the symmetry of the second fundamental form, but a certain kind of global symmetry. Because this global symmetry was a character to weaken the definition of reflective submanifold, it was named weakly reflective submanifold and examined its basic property. Weakly reflective submanifolds are austere submanifolds, and austere submanifolds are minimal submanifolds. The weakly reflective orbits was able to be classified in addition to the classification of the above-mentioned austere orbits. It is shown that the orbit with degenerate Gauss map becomes a weakly reflective subman … More ifold, and has generalized this though there was a result that the orbit of cohomogeneity 1 with degenerate Gauss map becomes austere before. That is, orbits with degenerate Gauss map are weakly reflective, and weakly reflective orbits are austere.The research of the orbits of linear isotoropy action of Riemann symmetry pairs is important to lead various relations concerning kinematic formula and the quermassintegrals in real space forms and complex space forms. Actually, the concept of the multiple Kaehler angle that the representative introduced was able to be led from the viewpoint of geometry of the orbit naturally, and when kinematic formula in complex space forms was formulated, the character to have obtained from geometrical consideration in the orbit played a basic role. In addition, a multiple Kaehler angle and its basic properties are important bases in the re-construction of integral geometry that makes the concept of valuation that has progressed in the past, several years a base. The viewpoint of geometry of the orbit is indispensable to research integral geometry in this direction of the future. Less

在同质空间中的积分几何形状的研究中，在线性同位素作用的轨道上，关键的示例是sustere submanifolds。球体，但一种全球对称性。要分类到分类F的局部局部性，表明具有脱名的高斯映射的轨道变成了一个弱反映的子人物，即带有脱胶​​高斯映射的Thomegeneine 1具有弱反射性的轨道。 IRS对于在某些Y中引导运动学公式和QuermassSintegrals是重要的，当您的多个Kaehler角的概念中，当在复杂空间配方c角色中，可以从轨道上d的角度来指导表示。角度ATS基本特性是重建ntegral几何形状的重要基础，这使得这使得thakes过去在过去的估值中，几年是轨道的观点。未来的方向。

项目成果

Flat fronts in hyperbolic 3-space and their caustics

• DOI: 10.2969/jmsj/1180135510
• 发表时间: 2005-11
• 期刊: Journal of The Mathematical Society of Japan
• 影响因子: 0.7
• 作者: M. Kokubu;W. Rossman;M. Umehara;Kotaro Yamada

積分の近似和の収束の速さ

近似积分和的收敛速度

• 发表时间: 2008
• 作者: Kokubu;Masatoshi; Rossman;Wayne; Umehara;Masaaki; Yamada;Kotaro;Mitsuhiro Itoh;Masatoshi Kokubu;Hiroyuki Tasaki;Katsuhiro Moriya;Katsuya Mashimo;Koji Tojo;田崎博之
• 通讯作者: 田崎博之

Classification of totally real and totally geodesic submanifolds of comnpact 5-symmetric spaces

紧五对称空间全实数和全测地线子流形的分类

• 发表时间: 2006
• 期刊: Journal of Mathematical Society of Japan 58・1
• 作者: Kokubu;Masatoshi; Rossman;Wayne; Umehara;Masaaki; Yamada;Kotaro;Mitsuhiro Itoh;Masatoshi Kokubu;Hiroyuki Tasaki;Katsuhiro Moriya;Katsuya Mashimo;Koji Tojo
• 通讯作者: Koji Tojo

A space of minimal tori with one end and cyclic symmetry

具有一端且循环对称的最小环面空间

• 发表时间: 2006
• 期刊: Tsukuba Journal of Mathematics 30・1
• 作者: Kokubu;Masatoshi; Rossman;Wayne; Umehara;Masaaki; Yamada;Kotaro;Mitsuhiro Itoh;Masatoshi Kokubu;Hiroyuki Tasaki;Katsuhiro Moriya
• 通讯作者: Katsuhiro Moriya

The Serre Duality for Holomorphic Vector Bundles over Strongly Pseudo Convex CR Manifolds

强伪凸CR流形上全纯向量束的Serre对偶性

• 发表时间: 2007
• 期刊: Proceedings of the Eleventh International Workshop on Diff. Geom. 11
• 作者: Kokubu;Masatoshi; Rossman;Wayne; Umehara;Masaaki; Yamada;Kotaro;Mitsuhiro Itoh
• 通讯作者: Mitsuhiro Itoh