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Conformal Geometry and Dynamics

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Conformal holonomy of bi-invariant metrics


Author: Felipe Leitner
Journal: Conform. Geom. Dyn. 12 (2008), 18-31
MSC (2000): Primary 53A30, 53C29; Secondary 53B15
DOI: https://doi.org/10.1090/S1088-4173-08-00175-6
Published electronically: March 5, 2008
MathSciNet review: 2385406
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Abstract: We discuss in this paper the conformal geometry of bi-invariant metrics on compact semisimple Lie groups. For this purpose, we develop an invariant Cartan calculus. Our main goal is to derive an iterative formula for the holonomy algebra of the normal conformal Cartan connection of a bi-invariant metric. As an example, we demonstrate the application of our invariant calculus to the computation of the conformal holonomy of $ \mathrm{SO}(4)$. Its conformal holonomy algebra is $ \mathfrak{so}(7)$.


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Additional Information

Felipe Leitner
Affiliation: Institut für Geometrie und Topologie, Universität Stuttgart, Pfaffenwaldring 57, Stuttgart-Vaihingen, D-70569, Germany
Email: leitner@mathematik.uni-stuttgart.de

DOI: https://doi.org/10.1090/S1088-4173-08-00175-6
Keywords: Conformal geometry, holonomy theory
Received by editor(s): April 19, 2007
Published electronically: March 5, 2008
Article copyright: © Copyright 2008 American Mathematical Society

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