[Fibrés homogènes et première valeur propre sur les espaces symétriques]
On montre que le point de Gieseker d’un fibré homogène irréductible sur un espace homogène rationnel est stable. On en déduit une majoration optimale de la première valeur propre du laplacien d’une métrique Kählérienne quelconque sur un espace symétrique Hermitien compact du type ABDC.
In this note we prove the stability of the Gieseker point of an irreducible homogeneous bundle over a rational homogeneous space. As an application we get a sharp upper estimate for the first eigenvalue of the Laplacian of an arbitrary Kähler metric on a compact Hermitian symmetric spaces of ABCD–type.
Keywords: Homogeneous bundles, spectrum of the Laplacian
Mot clés : fibrés homogènes, spectre du Laplacien
@article{AIF_2008__58_7_2315_0,
author = {Biliotti, Leonardo and Ghigi, Alessandro},
title = {Homogeneous bundles and the first eigenvalue of symmetric spaces},
journal = {Annales de l'Institut Fourier},
pages = {2315--2331},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {58},
number = {7},
year = {2008},
doi = {10.5802/aif.2415},
zbl = {1161.53064},
mrnumber = {2498352},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2415/}
}
TY - JOUR AU - Biliotti, Leonardo AU - Ghigi, Alessandro TI - Homogeneous bundles and the first eigenvalue of symmetric spaces JO - Annales de l'Institut Fourier PY - 2008 SP - 2315 EP - 2331 VL - 58 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2415/ DO - 10.5802/aif.2415 LA - en ID - AIF_2008__58_7_2315_0 ER -
%0 Journal Article %A Biliotti, Leonardo %A Ghigi, Alessandro %T Homogeneous bundles and the first eigenvalue of symmetric spaces %J Annales de l'Institut Fourier %D 2008 %P 2315-2331 %V 58 %N 7 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2415/ %R 10.5802/aif.2415 %G en %F AIF_2008__58_7_2315_0
Biliotti, Leonardo; Ghigi, Alessandro. Homogeneous bundles and the first eigenvalue of symmetric spaces. Annales de l'Institut Fourier, Tome 58 (2008) no. 7, pp. 2315-2331. doi : 10.5802/aif.2415. http://www.numdam.org/articles/10.5802/aif.2415/
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