2011 Fiscal Year Final Research Report
Differential geometry and integral geometry in homogeneous spaces and its applications
| Project/Area Number |
21540063
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
ITOH Mitsuhiro 筑波大学, 名誉教授 (40015912)
IKAWA Osamu 福島工業高等専門学校, 一般教科, 教授 (60249745)
SAKAI Takashi 首都大学東京, 理工学研究科, 准教授 (30381445)
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| Research Collaborator |
TANAKA Makiko 東京理科大学, 理工学部, 准教授 (20255623)
IRIYEH Hiroshi 東京電機大学, 未来科学部, 准教授 (30385489)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 微分幾何学 / 積分幾何学 / 等質空間 / 部分多様体 / Hermite対称空間 / 実形 / 対蹠集合 |
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| Research Abstract |
We proved that the intersection of two real forms in a Hermitian symmetric space of compact type is an antipodal set in a joint work with Makiko Tanaka and investigated their intersection by the use of the theory of polars introduced by Chen-Nagano. Using this result we determined the Floer homology of two real forms and extended Arnold-Givental inequalities in a joint work with Hiroshi Iriyeh and Takashi Sakai. Moreover we used these results and a kinematic formula to obtain an estimate of the volume of Hamiltonian deformation of a real form from below.
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