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Bruce Gilligan; Karl Oeljeklaus
Two remarks on Kähler homogeneous manifolds
Annales de la faculté des sciences de Toulouse Sér. 6, 17 no. 1 (2008), p. 73-80, doi: 10.5802/afst.1176
Article: subscription required (your ip address: 23.22.76.170) | Reviews MR 2464094 | Zbl 1160.32023
[1] Akhiezer (D.).— Invariant analytic hypersurfaces in complex nilpotent Lie groups, Ann. Global Anal. Geom., 2, p. 129-140 (1984). MR 777904 | Zbl 0576.32039
[2] Akhiezer (D.).— Invariant meromorphic functions on complex semisimple Lie groups, Invent. Math. 65, p. 325-329 (1982). MR 643557 | Zbl 0479.32010
[3] Berteloot (F.).— Existence d’une structure kählérienne sur les variétés homogènes semi-simples, C.R. Acad. Sci. Paris, Sér. I, 305, p. 809-812 (1987). Zbl 0635.32019
[4] Borel (A.) and Remmert (R.).— Über kompakte homogene Kählersche Mannigfaltigkeiten, Math. Ann. 145, p. 429-439 (1962). MR 145557 | Zbl 0111.18001
[5] Gilligan (B.) and Huckleberry (A. T.).— On Non-Compact Complex Nil-Manifolds, Math. Ann. 238, p. 39-49 (1978). MR 510305 | Zbl 0405.32009
[6] Hochschild (G.) and Mostow (G.D.).— On the algebra of representative functions of an analytic group. II, Amer. J. Math., 86, p. 869-887 (1964). MR 200392 | Zbl 0152.01301
[7] Huckleberry (A.) and Oeljeklaus (E.).— On holomorphically separable complex solvmanifolds, Ann. Inst. Fourier (Grenoble) 36, p. 57-65 (1986).
Cedram | MR 865660 | Zbl 0571.32012
[8] Loeb (J-J).— Fonctions plurisousharmoniques sur un groupe de Lie complexe invariantes par une forme réelle, C.R. Acad. Sci. Paris, Sér. I, 299, p. 663-666 (1984). MR 770458 | Zbl 0616.31006
[9] Matsushima (Y.).— Espaces homogènes de Stein des groupes de Lie complexes, Nagoya Math. J. 16, p. 205-218 (1960).
Article | MR 109854 | Zbl 0094.28201
[10] Onishchik (A. L.).— Complex envelopes of compact homogeneous spaces, Dokl. Acad. Nauk SSSR 130, p. 726-729 (1960). Zbl 0090.09401
[11] Oeljeklaus (K.) and Richthofer (W.).— On the Structure of Complex Solvmanifolds, J. Diff. Geom. 27, p. 399-421 (1988).
Article | MR 940112 | Zbl 0619.32021
[12] Oeljeklaus (K.) and Richthofer (W.).— Recent results on homogeneous complex manifolds. Complex Analysis III, (College Park, Md., 1985-86), p. 78-119, Lecture Notes in Math. 1277, Springer, Berlin, 1987. MR 922335 | Zbl 0627.32026
Bruce Gilligan; Karl Oeljeklaus
Two remarks on Kähler homogeneous manifolds
Annales de la faculté des sciences de Toulouse Sér. 6, 17 no. 1 (2008), p. 73-80, doi: 10.5802/afst.1176
Article: subscription required (your ip address: 23.22.76.170) | Reviews MR 2464094 | Zbl 1160.32023
Résumé - Abstract
We prove that every Kähler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger version of a question posed by Akhiezer for homogeneous spaces of nonsolvable algebraic groups in the case where the isotropy has the property that its intersection with the radical is Zariski dense in the radical.
Bibliography
[2] Akhiezer (D.).— Invariant meromorphic functions on complex semisimple Lie groups, Invent. Math. 65, p. 325-329 (1982). MR 643557 | Zbl 0479.32010
[3] Berteloot (F.).— Existence d’une structure kählérienne sur les variétés homogènes semi-simples, C.R. Acad. Sci. Paris, Sér. I, 305, p. 809-812 (1987). Zbl 0635.32019
[4] Borel (A.) and Remmert (R.).— Über kompakte homogene Kählersche Mannigfaltigkeiten, Math. Ann. 145, p. 429-439 (1962). MR 145557 | Zbl 0111.18001
[5] Gilligan (B.) and Huckleberry (A. T.).— On Non-Compact Complex Nil-Manifolds, Math. Ann. 238, p. 39-49 (1978). MR 510305 | Zbl 0405.32009
[6] Hochschild (G.) and Mostow (G.D.).— On the algebra of representative functions of an analytic group. II, Amer. J. Math., 86, p. 869-887 (1964). MR 200392 | Zbl 0152.01301
[7] Huckleberry (A.) and Oeljeklaus (E.).— On holomorphically separable complex solvmanifolds, Ann. Inst. Fourier (Grenoble) 36, p. 57-65 (1986).
Cedram | MR 865660 | Zbl 0571.32012
[8] Loeb (J-J).— Fonctions plurisousharmoniques sur un groupe de Lie complexe invariantes par une forme réelle, C.R. Acad. Sci. Paris, Sér. I, 299, p. 663-666 (1984). MR 770458 | Zbl 0616.31006
[9] Matsushima (Y.).— Espaces homogènes de Stein des groupes de Lie complexes, Nagoya Math. J. 16, p. 205-218 (1960).
Article | MR 109854 | Zbl 0094.28201
[10] Onishchik (A. L.).— Complex envelopes of compact homogeneous spaces, Dokl. Acad. Nauk SSSR 130, p. 726-729 (1960). Zbl 0090.09401
[11] Oeljeklaus (K.) and Richthofer (W.).— On the Structure of Complex Solvmanifolds, J. Diff. Geom. 27, p. 399-421 (1988).
Article | MR 940112 | Zbl 0619.32021
[12] Oeljeklaus (K.) and Richthofer (W.).— Recent results on homogeneous complex manifolds. Complex Analysis III, (College Park, Md., 1985-86), p. 78-119, Lecture Notes in Math. 1277, Springer, Berlin, 1987. MR 922335 | Zbl 0627.32026
