2013 Fiscal Year Final Research Report
Principal curvatures and topology of codimension-one isometric immersions of complete manifolds into the spaces of constant holomorphic curvatures.
| Project/Area Number |
22540106
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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 | Fukuoka University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
KAWAKUBO Satoshi 福岡大学, 理学部, 助教 (80360303)
MATSUURA Nozomu 福岡大学, 理学部, 助教 (00389339)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | リーマン計量 / 主曲率 / フィンスラー多様体 / 測地線 / ハウスドルフ距離 |
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| Research Abstract |
We have succeeded in classifying all of the curvature adopted complete real hyper surfaces in the hyperbolic spaces with constant holomorphic sectional curvature.
It should be emphasized that the constancy of the principal curvatures is not assumed but a consequence. The back ground of the investigation is the critical point theory of distance functions. Our idea applies to the study of the Rauch conjecture on the cut loci and conjugate loci of complete manifolds and of the Alexandrov-Toponogov comparison theorem under the radial curvature assumption.
As a consequence, we have obtained new types of topological sphere theorems under various model surfaces. These results will be useful for the study of convexity on inner metric spaces. Thus, the global study of Riemannian-Finsler Geometry will be seen.
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Research Products
(20 results)
