2017 Fiscal Year Final Research Report
Affine immersions in various fields
| Project/Area Number |
26400058
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Hokkaido University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
FUJIOKA Atsushi 関西大学, システム理工学部, 教授 (30293335)
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| Research Collaborator |
HASEGAWA Izumi
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 射影はめ込み / 中心アファインはめ込み / 統計多様体 / 正則統計多様体 / CR部分多様体 / 佐々木統計多様体 / 剱持統計多様体 |
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| Outline of Final Research Achievements |
We showed that a nondegenerate surface in the projective 3-space is locally constructed from a centroaffine minimal surface in the 4-dimensional vector space. The condition for such a surface to be projectively applicable to an affine sphere was obtained. We determined a nondegenerate centroaffine ruled surface such that the image of its center map lies on a plane containing the origin.
We defined the sectional curvature for a statistical structure, and found several properties of CR statistical submanifolds in a holomorphic statistical manifold of constant holomorphic sectional curvature, which are similar to well-known results for CR submanifolds in a Kaehler space form. We introduced notions of Sasakian statistical structure and Kenmotsu statistical structure, and gave their interesting examples.
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| Free Research Field |
微分幾何学
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