Semistability of invariant bundles over $ G/\Gamma $, II

Indranil Biswas

doi:10.1016/j.crma.2012.02.011

Analytic Geometry

Semistability of invariant bundles over

G / Γ

, II

Presented by: Jean-Pierre Demailly

Indranil Biswas ¹

¹ School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India

Comptes Rendus. Mathématique, Volume 350 (2012) no. 5-6, pp. 277-280.

Abstract
Résumé

Let G be a connected complex Lie group, and let Γ be a cocompact discrete subgroup of G. We prove that any invariant principal bundle on $G / Γ$ is semistable with respect to any Hermitian structure on $G / Γ$ given by some right-translation invariant Hermitian structure on G.

Soit G un groupe de Lie connexe sur $C$ , et soit $Γ \subset G$ un sous-groupe discret cocompact. Nous démontrons que tout fibré vectoriel invariant sur $G / Γ$ est semi-stable par rapport à toute structure hermitienne sur $G / Γ$ provenant dʼune structure hermitienne sur G invariante par translations à droite.

Received: 2011-11-28
Accepted: 2012-02-28
Published online: 2012-03-01

DOI: 10.1016/j.crma.2012.02.011

Author's affiliations:

Indranil Biswas ¹

¹ School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India

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     title = {Semistability of invariant bundles over $ G/\Gamma $, {II}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {277--280},
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     volume = {350},
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     year = {2012},
     doi = {10.1016/j.crma.2012.02.011},
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Indranil Biswas. Semistability of invariant bundles over $ G/\Gamma $, II. Comptes Rendus. Mathématique, Volume 350 (2012) no. 5-6, pp. 277-280. doi : 10.1016/j.crma.2012.02.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.02.011/

References
Cited by

[1] I. Biswas Semistability of invariant bundles over $G / Γ$ , C. R. Acad. Sci. Paris, Ser. I, Volume 349 (2011), pp. 1187-1190

[2] S. Kobayashi Differential Geometry of Complex Vector Bundles, Publications of the Mathematical Society of Japan, vol. 15, Iwanami Shoten Publishers and Princeton University Press, 1987

[3] M.S. Raghunathan Discrete Subgroups of Lie Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 68, Springer-Verlag, New York–Heidelberg, 1972

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