2014 Fiscal Year Final Research Report
An approach to cellular decompositions of hyperbolic manifolds based on variational principles
| Project/Area Number |
24540071
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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 | Kanazawa University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 幾何学 / 双曲幾何学 |
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| Outline of Final Research Achievements |
A variational principle is a principle that is used to obtain a “best” solution of a given family of functions. The purpose of this research project was set to obtain a sufficient decomposition of a hyperbolic manifold, which is a subject of geometry, using a variational principle.
During this research project, I published a research article about a behavior of the volumes of orthoschemes, that is used to decompose hyperbolic manifolds and is a generalization of pyramids in the Euclidean space. Its main result explains the difference of the behavior of the volume from the Euclidean one, when the “height” of the orthoscheme varies. This research was obtained from the Schlaefli formula, a variation of the variational principle with respect to the hyperbolic volume form. Not only publishing the result, it was also presented in domestic and international conferences for mathematics.
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| Free Research Field |
数学
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