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Curvilinear coordinates on generic conformally flat hypersurfaces and constant curvature 2-metrics
被引：5
作者：
Burstall, Francis E.
[1
]
Hertrich-Jeromin, Udo
[2
]
Suyama, Yoshihiko
[3
]
机构：
[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England
[2] Tech Univ Wien, E104,Wiedner Haupstr 8-10, A-1040 Vienna, Austria
[3] Fukuoka Univ, Dept Appl Math, Fukuoka 8140180, Japan
关键词：
conformally flat hypersurface;
surface metric with constant Gauss curvature-1;
Guichard net;
system of evolution equations;
EUCLIDEAN;
4-SPACE;
GUICHARD NET;
D O I：
10.2969/jmsj/07027420
中图分类号：
O1 [数学];
学科分类号：
0701 ;
070101 ;
摘要：
There is a one-to-one correspondence between associated families of generic conformally flat (local-)hypersurfaces in 4-dimensional space forms and conformally flat 3-metrics with the Guichard condition. In this paper, we study the space of conformally flat 3-metrics with the Guichard condition: 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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页码：617 / 649
页数：33
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