Homogeneous bundles and the first eigenvalue of symmetric spaces
Annales de l'Institut Fourier, Volume 58 (2008) no. 7, pp. 2315-2331.

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.

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.

DOI: 10.5802/aif.2415
Classification: 53C55,  32M10
Keywords: Homogeneous bundles, spectrum of the Laplacian
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, Volume 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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