Diameter of \(SU_2\) for a left-invariant axisymmetric Riemannian metric

Diameter of \(SU_2\) for a left-invariant axisymmetric Riemannian metric

We consider the Lie group \(SU_2\) endowed with a left-invariant axisymmetric Riemannian metric. This means that a metric has eigenvalues \(I_1 = I_2, I_3 > 0\). We give an explicit formula for the diameter of such metric. Other words, we compute the diameter of Berger's sphere.

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Veröffentlicht in:arXiv.org 2017-10
1. Verfasser: Podobryaev, A V
Format: Artikel
Sprache:eng
Schlagworte:
Eigenvalues
Invariants
Lie groups
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Zusammenfassung:We consider the Lie group \(SU_2\) endowed with a left-invariant axisymmetric Riemannian metric. This means that a metric has eigenvalues \(I_1 = I_2, I_3 > 0\). We give an explicit formula for the diameter of such metric. Other words, we compute the diameter of Berger's sphere.
ISSN:2331-8422
DOI:10.48550/arxiv.1710.02945