Grassmann geometry on the 3-dimensional unimodular Lie groups I

被引：3
|
作者：
Inoguchi, Jun-ichi [1 ]
Naitoh, Hiroo [2 ]
机构：
[1] Yamagata Univ, Fac Sci, Dept Math Sci, Yamagata 9908560, Japan
[2] Yamaguchi Univ, Dept Math, Yamaguchi 7538512, Japan
来源：
HOKKAIDO MATHEMATICAL JOURNAL | 2009年 / 38卷 / 03期
关键词：
Grassmann geometry; unimodular Lie group; Heisenberg group; Euclidean plane; Minkowski plane; special unitary group; special linear group; totally geodesic surface; flat surface; minimal surface; surface of constant mean curvature; PARALLEL SURFACES; SPACES;
D O I：
10.14492/hokmj/1258553972
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the Grassmann geometry of surfaces when the ambient space is a 3-dimensional unimodular Lie group with left invariant metric, that is, it is one of the 3-dimensional commutative Lie group, the 3-dimensional Heisenberg group, the groups of rigid motions on the Euclidean or the Minkowski planes, the special unitary group SU(2), and the special real linear group SL(2, R).
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页码：427 / 496
页数：70
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