Given A∈ Ωₙ, the n²-dimensional spectral unit ball, we show that if B is an n×n complex matrix, then B is a “generalized” tangent vector at A to an entire curve in Ωₙ if and only if B is in the tangent cone to the isospectral variety at A. In the case of Ω₃, the zero set of the Kobayashi-Royden pseudometric is completely described.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-1-4,
author = {Nikolai Nikolov and Pascal J. Thomas},
title = {On the zero set of the Kobayashi-Royden pseudometric of the spectral unit ball},
journal = {Annales Polonici Mathematici},
volume = {93},
year = {2008},
pages = {53-68},
zbl = {1144.32003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-1-4}
}
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) pp. 53-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-1-4/