2017 Fiscal Year Final Research Report
Research for duality and transformations of generic conformally flat hypersurfaces.
| Project/Area Number |
26400076
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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 | Fukuoka University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | conformally flat / Guichard net / duality / conformally invariant / constant Gauss curvature / hypersurfaces / evolution equation |
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| Outline of Final Research Achievements |
There is a canonical one-to-one correspondence between generic conformally flat (local-)hypersurfaces and conformally flat 3-metrics with the Guichard condition. We have studied the space of conformally flat 3-metric with the Guichard condition. The most important result in this study is as follows: for a conformally flat 3-metric with the Guichard condition in the interior of the space, an evolution of orthogonal (local-)Riemannian 2-metrics with constant Gauss curvature -1 is determined; for a 2-metric belonging to a certain class of orthogonal analytic 2-metrics with constant Gauss curvature -1, a one-parameter family of conformally flat 3-metrics with the Guichard condition is determined as evolutions issuing from the 2-metric.
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| Free Research Field |
微分幾何学
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