Geodesic
On the zero set of the Kobayashi–Royden pseudometric of the spectral unit ball
Nikolai Nikolov1 ; Pascal J. Thomas2
1 Institute of Mathematics and Informatics Bulgarian Academy of Sciences Acad. G. Bonchev 8 1113 Sofia, Bulgaria
2 Laboratoire Émile Picard UMR CNRS 5580 Université Paul Sabatier 118 Route de Narbonne F-31062 Toulouse Cedex, France
Annales Polonici Mathematici, Tome 93 (2008) no. 1, pp. 53-68 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Given $A\in {\mit\Omega} _n,$ the $n^2$-dimensional spectral unit ball, we show that if $B$ is an $n\times n$ complex matrix, then $B$ is a “generalized” tangent vector at $A$ to an entire curve in ${\mit\Omega} _n$ if and only if $B$ is in the tangent cone $C_A$ to the isospectral variety at $A.$ In the case of ${\mit\Omega} _3,$ the zero set of the Kobayashi–Royden pseudometric is completely described.
DOI : 10.4064/ap93-1-4
Keywords: given mit omega dimensional spectral unit ball times complex matrix generalized tangent vector entire curve mit omega only tangent cone isospectral variety mit omega zero set kobayashi royden pseudometric completely described

Nikolai Nikolov 1 ; Pascal J. Thomas 2

1 Institute of Mathematics and Informatics Bulgarian Academy of Sciences Acad. G. Bonchev 8 1113 Sofia, Bulgaria
2 Laboratoire Émile Picard UMR CNRS 5580 Université Paul Sabatier 118 Route de Narbonne F-31062 Toulouse Cedex, France 
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Nikolai Nikolov; Pascal J. Thomas. On the zero set of the Kobayashi–Royden pseudometric
 of the spectral unit ball. Annales Polonici Mathematici, Tome 93 (2008) no. 1, pp. 53-68. doi: 10.4064/ap93-1-4

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