Adapted complex structures and Riemannian homogeneous spaces

Róbert Szőke

Annales Polonici Mathematici (1998)

  • Volume: 70, Issue: 1, page 215-220
  • ISSN: 0066-2216

Abstract

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We prove that every compact, normal Riemannian homogeneous manifold admits an adapted complex structure on its entire tangent bundle.

How to cite

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Róbert Szőke. "Adapted complex structures and Riemannian homogeneous spaces." Annales Polonici Mathematici 70.1 (1998): 215-220. <http://eudml.org/doc/262676>.

@article{RóbertSzőke1998,
abstract = {We prove that every compact, normal Riemannian homogeneous manifold admits an adapted complex structure on its entire tangent bundle.},
author = {Róbert Szőke},
journal = {Annales Polonici Mathematici},
keywords = {adapted complex structures; Riemannian homogeneous spaces; homogeneous manifold; adapted complex structure},
language = {eng},
number = {1},
pages = {215-220},
title = {Adapted complex structures and Riemannian homogeneous spaces},
url = {http://eudml.org/doc/262676},
volume = {70},
year = {1998},
}

TY - JOUR
AU - Róbert Szőke
TI - Adapted complex structures and Riemannian homogeneous spaces
JO - Annales Polonici Mathematici
PY - 1998
VL - 70
IS - 1
SP - 215
EP - 220
AB - We prove that every compact, normal Riemannian homogeneous manifold admits an adapted complex structure on its entire tangent bundle.
LA - eng
KW - adapted complex structures; Riemannian homogeneous spaces; homogeneous manifold; adapted complex structure
UR - http://eudml.org/doc/262676
ER -

References

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  2. [Be] A. L. Besse, Einstein Manifolds, Springer, 1987. 
  3. [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. Zbl0921.32006
  4. [G-S] V. Guillemin and M. Stenzel, Grauert tubes and the homogeneous Monge-Ampère equation I, J. Differential Geom. 34 (1991), 561-570. Zbl0746.32005
  5. [Ka] S. J. Kan, On the rigidity of non-positively curved Grauert tubes, preprint, 1996. 
  6. [Ka2] S. J. Kan, The asymptotic expansion of a CR invariant and Grauert tubes, Math. Ann. 304, (1996), 63-92. Zbl0848.32004
  7. 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. Zbl0752.32008
  8. [Ma] Y. Matsushima, Espaces homogènes de Stein des groupes de Lie complexes, Nagoya Math. J. 16 (1960), 205-218. Zbl0094.28201
  9. [M] G. D. Mostow, Some new decomposition theorems for semi-simple groups, Mem. Amer. Math. Soc. 4 (1955), 31-54. Zbl0064.25901
  10. [Sz] R. Szőke, Complex structures on the tangent bundle of Riemannian manifolds, Math. Ann. 291 (1991), 409-428. Zbl0749.53021
  11. [Sz2] R. Szőke, Automorphisms of certain Stein manifolds, Math. Z. 219 (1995), 357-385. Zbl0829.32009
  12. [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. 

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