Comptes Rendus
no. 5-6
Analytic Geometry
Semistability of invariant bundles over G/Γ, II
Jean-Pierre Demailly
Indranil Biswas1
1School 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

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⊂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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.02.011

Indranil Biswas  1

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