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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Published in | Journal of the Korean Mathematical Society Vol. 58; no. 6; pp. 1407 - 1419 |
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Main Author | |
Format | Journal Article |
Language | Korean |
Published |
2021
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Subjects | |
Online Access | Get full text |
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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. |
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Bibliography: | KISTI1.1003/JNL.JAKO202131452790710 |
ISSN: | 0304-9914 |