Quaternionic-Kähler geometry and almost Kähler A-manifolds

Włodzimierz Jelonek

Annales Polonici Mathematici (2000)

  • Volume: 75, Issue: 2, page 111-124
  • ISSN: 0066-2216

Abstract

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The aim of this paper is to give an easy explicit description of 3-K-contact structures on certain SO(3)-principal fibre bundles over quaternionic-Kähler manifolds.

How to cite

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Jelonek, Włodzimierz. "Quaternionic-Kähler geometry and almost Kähler A-manifolds." Annales Polonici Mathematici 75.2 (2000): 111-124. <http://eudml.org/doc/208389>.

@article{Jelonek2000,
abstract = {The aim of this paper is to give an easy explicit description of 3-K-contact structures on certain SO(3)-principal fibre bundles over quaternionic-Kähler manifolds.},
author = {Jelonek, Włodzimierz},
journal = {Annales Polonici Mathematici},
keywords = {quaternionic-Kähler manifold; contact structure; principal fibre bundle; 3-Sasakian manifold},
language = {eng},
number = {2},
pages = {111-124},
title = {Quaternionic-Kähler geometry and almost Kähler A-manifolds},
url = {http://eudml.org/doc/208389},
volume = {75},
year = {2000},
}

TY - JOUR
AU - Jelonek, Włodzimierz
TI - Quaternionic-Kähler geometry and almost Kähler A-manifolds
JO - Annales Polonici Mathematici
PY - 2000
VL - 75
IS - 2
SP - 111
EP - 124
AB - The aim of this paper is to give an easy explicit description of 3-K-contact structures on certain SO(3)-principal fibre bundles over quaternionic-Kähler manifolds.
LA - eng
KW - quaternionic-Kähler manifold; contact structure; principal fibre bundle; 3-Sasakian manifold
UR - http://eudml.org/doc/208389
ER -

References

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  1. [A-G-I] B. Alexandrov, G. Grantcharov and S. Ivanov, Curvature properties of twistor spaces of quaternionic-Kähler manifolds, J. Geometry 62 (1998), 1-12. Zbl0911.53019
  2. [B] A. Besse, Einstein Manifolds, Springer, Berlin, 1987. 
  3. [D-N] J. E. D'Atri and H. K. Nickerson, Divergence-preserving geodesic symmetries, J. Differential Geom. 3 (1969), 467-476. Zbl0195.23604
  4. [D-M] J. Davidov and O. Muskarov, Twistor spaces with Hermitian Ricci tensor, Proc. Amer. Math. Soc. 109 (1990), 1115-1120. Zbl0704.53051
  5. [E-S] J. Eells et S. Salamon, Constructions twistorielles des applications harmo- niques, C. R. Acad. Sci. Paris 296 (1983), 685-687. Zbl0531.58020
  6. [G-L] K. Galicki and H. B. Lawson, Quaternionic reduction and quaternionic orbifolds, Math. Ann. 282 (1988), 1-21. Zbl0628.53060
  7. [Go] S. I. Goldberg, The integrability of almost Kähler structures, Proc. Amer. Math. Soc. 21 (1969), 96-100. 
  8. [G] A. Gray, Einstein like manifolds which are not Einstein, Geom. Dedicata 7 (1978), 259-280. Zbl0378.53018
  9. [J-1] W. Jelonek, Self-duality and A-manifolds, J. London Math. Soc. 58 (1998), 697-708. 
  10. [J-2] W. Jelonek, K-contact A-manifolds, Colloq. Math. 75 (1998), 97-103. 
  11. [J-3] W. Jelonek, Almost Kähler A-structures on twistor bundles, Ann. Global Anal. Geom. 17 (1999), 329-339. Zbl0982.53045
  12. [K] M. Konishi, On manifolds with Sasakian 3-structures over quaternionic-Kähler manifolds, Kodai Math. Sem. Rep. 26 (1975), 194-200. Zbl0308.53035
  13. [Ku] Y.-Y. Kuo, On almost contact 3-structures, Tôhoku Math. J. 22 (1970), 325-332. 
  14. [O'N] B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459-469. 
  15. [S] S. Salamon, Quaternionic Kähler manifolds, Invent. Math. 67 (1982), 143-171. Zbl0486.53048
  16. [Se] K. Sekigawa, On some compact Einstein almost Kähler manifolds, J. Math. Soc. Japan 36 (1987), 101-116. Zbl0668.53019
  17. [Sw] A. Swann, Hyperkähler and quaternionic Kähler geometry, Math. Ann. 289 (1991), 421-450. Zbl0711.53051
  18. [T] S. Tanno, Remarks on a triple of K-contact structures, Tôhoku Math. J. 48 (1996), 519-531. Zbl0881.53040
  19. [W] J. A. Wolf, Complex homogeneous contact manifolds and quaternionic symmetric spaces, J. Math. Mech. 14 (1965), 1033-1047. Zbl0141.38202

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