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Symmetric geodesics on conformal compactifications of Euclidean Jordan algebras

Published online by Cambridge University Press:  17 April 2009

Sang Youl Lee ,
Yongdo Lim  and
Chan-Young Park
Sang Youl Lee
Affiliation:
Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu 702-701, Korea e-mail: syleek@chollian.net
Yongdo Lim
Affiliation:
Topology and Geometry Research Center, Kyungpook National University, Taegu 702-701, Korea e-mail: ylim@math.kyungpook.ac.kr
Chan-Young Park
Affiliation:
Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu 702-701, Korea e-mail: chnypark@kyungpook.ac.kr
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Abstract

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In this article we define symmetric geodesies on conformal compactifications of Euclidean Jordan algebras and classify symmetric geodesics for the Euclidean Jordan algebra of all n × n symmetric real matrices. Furthermore, we show that the closed geodesics for the Euclidean Jordan algebra of all 2 × 2 symmetric real matrices are realised as the torus knots in the Shilov boundary of a Lie ball.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 187 - 201
Copyright
Copyright © Australian Mathematical Society 1999

References

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