Kodai Mathematical Journal

Complex contact manifolds and hyperkähler geometry

Brendan Foreman

Full-text: Open access

Article information

Source
Kodai Math. J., Volume 23, Number 1 (2000), 12-26.

Dates
First available in Project Euclid: 23 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1138044153

Digital Object Identifier
doi:10.2996/kmj/1138044153

Mathematical Reviews number (MathSciNet)
MR1749382

Zentralblatt MATH identifier
1028.53049

Subjects
Primary: 53C26: Hyper-Kähler and quaternionic Kähler geometry, "special" geometry
Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C56: Other complex differential geometry [See also 32Cxx] 53D10: Contact manifolds, general

Citation

Foreman, Brendan. Complex contact manifolds and hyperkähler geometry. Kodai Math. J. 23 (2000), no. 1, 12--26. doi:10.2996/kmj/1138044153. https://projecteuclid.org/euclid.kmj/1138044153


Export citation

References

  • [1] B. ALEKSANDROV, G. GRANTCHAROV AND S. IVANOV, Curvature properties of twistor spaces of quaternionic-Kahler manifolds, J. Geom., 64 (1998), 1-12.
  • [2] L. BERARD-BERGERY, Sur de nouvelles varietes emannienes d'Einstem, Institut Elie Cartan, 6, Univ. Nancy, 1982, 1-60
  • [3] A. BESSE, Einstein Manifolds, Springer, Berlin, 1986
  • [4] D. E. BLAIR, Contact Manifolds m Riemanman Geometry, Lecture Notes in Math., 509, Springer, Berlin-Heidelberg-New York, 1978
  • [5] W. M. BOOTHBY AND H. C. WANG, On contact manifolds, Ann. of Math., 68 (1958), 721 734.
  • [6] C. P. BOYER AND K. GALICKI, The twistor space of a 3-Sasakian manifold, Internat. J. Math., 8 (1997), 31-60
  • [7] M. FERNANDEZ AND A. GRAY, The Iwasawa manifold, Lecture Notes in Math., 1209, Springer, Berlin-Heidelberg-New York, 1986, 157-159
  • [8] B. FOREMAN, Vaational approaches to the geometry of complex contact geometry, preprint
  • [9] B. FOREMAN, Boothby-Wang fibrations on complex contact manifolds, to appear in Differ ential Geom. Appl.
  • [10] B. FOREMAN, Twistor spaces and complex contact Hermitian geometry, in preparation
  • [11] P. GRIFFITHS AND J. HARRIS, Principles of Algebraic Geometry, Wiley, New York, 1978
  • [12] Y. HATAKEYAMA, Some notes on differentiate manifolds with almost contact structures, Thoku Math. J., 15 (1963), 42-48
  • [13] S. ISHIHARA, Quaternion Kahlean manifolds and fibered Riemanman spaces with Sasakia 3-structure, Kodai Math. Sem. Rep., 25 (1973), 321-329.
  • [14] S. ISHIHARA AND M. KONISHI, Real contact 3-structure and complex contact structure, Southeast Asian Bull. Math., 3 (1979), 151-161
  • [15] S. ISHIHARA AND M. KONISHI, Differential Geometry of Fibred Spaces, Publications of Stud Group of Geometry, 8, Kyoto Univ., Kyoto, 1973.
  • [16] S. ISHIHARA AND M. KONISHI, Complex almost contact manifolds, Kodai Math. J., 3 (1980), 385-396
  • [17] S. ISHIHARA AND M. KONISHI, Complex almost contact structures in a complex contac manifold, Kodai Math. J, 5 (1982), 30-37
  • [18] S. KOBAYASHI, Remarks on complex contact manifolds, Proc. Amer. Math. Soc, 10 (1959), 164-16
  • [19] M. KONISHI, On manifolds with Sasakian 3-structure over quatermonic Kaehler manifolds, Kodai Math. Sem. Rep., 26 (1975), 194-200
  • [20] B. KARAMAN, Curvature and normality of complex contact manifolds, Thesis, Michigan Stat University.
  • [21] C. LEBRUN, Fano manifolds, contact structures, and quatermonic geometry, Internat. Math J., 6 (1995), 419-437.
  • [22] S. SALAMON, Quaterniomc-Kahler manifolds, Invent. Math., 67 (1982), 143-171
  • [23] R. STONG, Contact manifolds, J. Differential Geom., 9 (1974), 219-238
  • [24] R. O. WELLS, Differential Analysis on Complex Manifolds, Spnger, Berlin-Heidelberg-Ne York, 1980.