On the zero set of the Kobayashi--Royden pseudometric of the spectral unit ball

Nikolai Nikolov (1) , Pascal J. Thomas (2)

1 Institute of Mathematics and Informatics
2 IMT - Institut de Mathématiques de Toulouse UMR5219

Given $A\in\Omega_n,$ the $n^2$-dimensional spectral unit ball, we show that $B$ is a "generalized" tangent vector at $A$ to an entire curve in $\Omega_n$ if and only if $B$ is in the tangent cone $C_A$ to the isospectral variety at $A.$ In the case of $\Omega_3,$ the zero set of this metric is completely described.

Mots clés: invariant metrics; spectral ball

Domaines: Variables complexes [math.CV]

Nikolai Nikolov, Pascal J. Thomas. On the zero set of the Kobayashi--Royden pseudometric of the spectral unit ball. Annales Polonici Mathematici, 2008, 93 (1), pp.53-68. ⟨hal-00321221⟩