We prove that every compact, normal Riemannian homogeneous manifold admits an adapted complex structure on its entire tangent bundle.
@article{bwmeta1.element.bwnjournal-article-apmv70z1p215bwm,
author = {R\'obert Sz\H oke},
title = {Adapted complex structures and Riemannian homogeneous spaces},
journal = {Annales Polonici Mathematici},
volume = {69},
year = {1998},
pages = {215-220},
zbl = {0966.53038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv70z1p215bwm}
}
Róbert Szőke. Adapted complex structures and Riemannian homogeneous spaces. Annales Polonici Mathematici, Tome 69 (1998) pp. 215-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv70z1p215bwm/
[000] [B-D] T. Bröcker and T. tom Dieck, Representations of Compact Lie Groups, Springer, New York, 1985. | Zbl 0581.22009
[001] [Be] A. L. Besse, Einstein Manifolds, Springer, 1987.
[002] [Bu] D. Burns, On the uniqueness and characterization of Grauert tubes, in: Complex Analysis and Geometry, V. Ancona, E. Ballico and A. Silva (eds.), Marcel Dekker, 1996, 119-133. | Zbl 0921.32006
[003] [G-S] V. Guillemin and M. Stenzel, Grauert tubes and the homogeneous Monge-Ampère equation I, J. Differential Geom. 34 (1991), 561-570. | Zbl 0746.32005
[004] [Ka] S. J. Kan, On the rigidity of non-positively curved Grauert tubes, preprint, 1996.
[005] [Ka2] S. J. Kan, The asymptotic expansion of a CR invariant and Grauert tubes, Math. Ann. 304, (1996), 63-92. | Zbl 0848.32004
[006] L. Lempert and R. Szőke, Global solutions of the homogeneous complex Monge-Ampère equation and complex structures on the tangent bundle of Riemannian manifolds, Math. Ann. 291 (1991), 689-712. | Zbl 0752.32008
[007] [Ma] Y. Matsushima, Espaces homogènes de Stein des groupes de Lie complexes, Nagoya Math. J. 16 (1960), 205-218. | Zbl 0094.28201
[008] [M] G. D. Mostow, Some new decomposition theorems for semi-simple groups, Mem. Amer. Math. Soc. 4 (1955), 31-54. | Zbl 0064.25901
[009] [Sz] R. Szőke, Complex structures on the tangent bundle of Riemannian manifolds, Math. Ann. 291 (1991), 409-428. | Zbl 0749.53021
[010] [Sz2] R. Szőke, Automorphisms of certain Stein manifolds, Math. Z. 219 (1995), 357-385. | Zbl 0829.32009
[011] [Sz3] R. Szőke, Adapted complex structures on tangent bundles of Riemannian manifolds, in: Complex Analysis and Generalized Functions (Varna, 1991), I. Dimovski and V. Hristov (eds.), Publ. House Bulgarian Acad. Sci., Sofia, 1993, 304-314.