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).

引用

页码：427 / 496

页数：70

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