Diameter of $S{U}_2$ for a left-invariant axisymmetric Riemannian metric

Abstract

We consider the Lie group $S{U}_2$ 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.

5 pages

References in corpus (1)

• Cut locus of a left invariant Riemannian metric on SO(3) in the axisymmetric case

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