no. 7
Homogeneous bundles and the first eigenvalue of symmetric spaces
[Fibrés homogènes et première valeur propre sur les espaces symétriques]
Biliotti, Leonardo1 ; Ghigi, Alessandro2
1 Università degli Studi di Parma Parma (Italia)
2 Università degli Studi di Milano Bicocca Milano (Italia)
Annales de l'Institut Fourier, Tome 58 (2008) no. 7, pp. 2315-2331.

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.

DOI : 10.5802/aif.2415
Classification : 53C55, 32M10
Keywords: Homogeneous bundles, spectrum of the Laplacian
Mot clés : fibrés homogènes, spectre du Laplacien

Biliotti, Leonardo 1 ; Ghigi, Alessandro 2

1 Università degli Studi di Parma Parma (Italia)
2 Università degli Studi di Milano Bicocca Milano (Italia) 
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2415/

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