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

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

2007-06-06

arxiv.org/abs/0706.0854v3

Ann. Pol. Math. 93 (2008), 53-68

Mathematics

Complex Variables

minor changes; to appear in Ann. Polon. Math

Scientific paper

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.

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