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 |
Section | 一般 |
Research Field |
Geometry
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Research Institution | Hokkaido University |
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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Project Status |
Completed (Fiscal Year 2017)
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Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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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 / 中心アファイン曲面 / 線織面 / 中心写像 / 概接触計量多様体 / 剱持多様体 / 捩じれ積 / 佐々木多様体 / 部分多様体 / アファインはめ込み / 射影曲面 / 断面曲率 / CR部分多様体 |
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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Report
(5 results)
Research Products
(20 results)
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[Journal Article] Sasakian statistical manifolds2017
Author(s)
Furuhata H., Hasegawa I., Okuyama Y., Sato K. and Shahid, M.H.
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Journal Title
J. Geom. Phys.
Volume: 117
Pages: 179-186
DOI
Related Report
Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
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[Presentation] 正則統計多様体とその曲率2014
Author(s)
古畑仁
Organizer
RIMS共同研究「統計多様体の諸分野への応用」
Place of Presentation
京都大学数理解析研究所(京都市)
Year and Date
2014-11-19
Related Report
Invited
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