RIEMANNIAN SUBMERSIONS OF SO 0 (2, 1)

The Iwasawa decomposition NAK of the Lie group G = SO0(2, 1) with a left invariant metric produces Riemannian submersions G → N\G, G → A\G, G → K\G, and G → NA\G. For each of these, we calculate the curvature of the base space and the lifting of a simple closed curve to the total space G. Especially...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 58; no. 6; pp. 1407 - 1419
Main Author Byun, Taechang
Format Journal Article
LanguageKorean
Published 2021
Subjects
solvable Lie group
nilpotent Lie group
principal bundle
area form
Lie algebra
Holonomy displacement
Riemannian submersion
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Summary:The Iwasawa decomposition NAK of the Lie group G = SO0(2, 1) with a left invariant metric produces Riemannian submersions G → N\G, G → A\G, G → K\G, and G → NA\G. For each of these, we calculate the curvature of the base space and the lifting of a simple closed curve to the total space G. Especially in the first case, the base space has a constant curvature 0; the holonomy displacement along a (null-homotopic) simple closed curve in the base space is determined only by the Euclidean area of the region surrounded by the curve.
Bibliography:KISTI1.1003/JNL.JAKO202131452790710
ISSN:0304-9914