Hokkaido Mathematical Journal

Grassmann geometry on the 3-dimensional unimodular Lie groups I

Jun-ichi INOGUCHI and Hiroo NAITOH

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Abstract

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 $SL(2,\mathbb R)$.

Article information

Source
Hokkaido Math. J., Volume 38, Number 3 (2009), 427-496.

Dates
First available in Project Euclid: 18 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1258553972

Digital Object Identifier
doi:10.14492/hokmj/1258553972

Mathematical Reviews number (MathSciNet)
MR2548231

Zentralblatt MATH identifier
1214.53016

Subjects
Primary: 53B25: Local submanifolds [See also 53C40]
Secondary: 53C40: Global submanifolds [See also 53B25] 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]

Keywords
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

Citation

INOGUCHI, Jun-ichi; NAITOH, Hiroo. Grassmann geometry on the 3-dimensional unimodular Lie groups I. Hokkaido Math. J. 38 (2009), no. 3, 427--496. doi:10.14492/hokmj/1258553972. https://projecteuclid.org/euclid.hokmj/1258553972


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