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Symmetric geodesics on conformal compactifications of Euclidean Jordan algebras. (English) Zbl 0977.53038

Summary: We define symmetric geodesics on conformal compactifications of Euclidean Jordan algebras and classify symmetric geodesics for the Euclidean Jordan algebra of all \(n\times n\) symmetric real matrices. Furthermore, we show that the closed geodesics for the Euclidean Jordan algebra of all \(2\times 2\) symmetric real matrices are realized as the torus knots in the Shilov boundary of a Lie ball.

MSC:

53C22 Geodesics in global differential geometry
57M25 Knots and links in the \(3\)-sphere (MSC2010)
53C35 Differential geometry of symmetric spaces
17C37 Associated geometries of Jordan algebras
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References:

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