A solution of a problem of Sophus Lie: normal forms of two-dimensional metrics admitting two projective vector fields

被引：52
作者：
Bryant, Robert L.
Manno, Gianni
Matveev, Vladimir S. [1 ]
机构：
[1] Math Inst, FSU Jena, D-07737 Jena, Germany
[2] Math Sci Res Inst, Berkeley, CA 94720 USA
[3] Dept Math, I-73100 Lecce, Italy
来源：
MATHEMATISCHE ANNALEN | 2008年 / 340卷 / 02期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1007/s00208-007-0158-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a complete list of normal forms for the two-dimensional metrics that admit a transitive Lie pseudogroup of geodesic-preserving transformations and we show that these normal forms are mutually non-isometric. This solves a problem posed by Sophus Lie.
引用
收藏
页码：437 / 463
页数：27
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