Hokkaido Mathematical Journal

Grassmann geometry on the 3-dimensional non-unimodular Lie groups

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 non-unimodular Lie group with left invariant metric. This work together with our previous papers yield a complete classification of Grassmann geometry of orbit type in all 3-dimensional homogeneous spaces.

Article information

Source
Hokkaido Math. J., Volume 48, Number 2 (2019), 385-406.

Dates
First available in Project Euclid: 11 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1562810516

Digital Object Identifier
doi:10.14492/hokmj/1562810516

Mathematical Reviews number (MathSciNet)
MR3980949

Zentralblatt MATH identifier
07080101

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

Keywords
Grassmann geometry non-unimodular Lie group

Citation

INOGUCHI, Jun-ichi; NAITOH, Hiroo. Grassmann geometry on the 3-dimensional non-unimodular Lie groups. Hokkaido Math. J. 48 (2019), no. 2, 385--406. doi:10.14492/hokmj/1562810516. https://projecteuclid.org/euclid.hokmj/1562810516


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