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http://dx.doi.org/10.4134/JKMS.j210025

RIEMANNIAN SUBMERSIONS OF SO0(2, 1)  

Byun, Taechang (Department of Mathematics and Statistics Sejong University)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.6, 2021 , pp. 1407-1419 More about this Journal
Abstract
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.
Keywords
Holonomy displacement; area form; Riemannian submersion; principal bundle; Lie algebra; nilpotent Lie group; solvable Lie group;
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Times Cited By KSCI : 1  (Citation Analysis)
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