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2004 | 2 | 5 | 732-753
Tytuł artykułu

Quaternionic and para-quaternionic CR structure on (4n+3)-dimensional manifolds

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We define notion of a quaternionic and para-quaternionic CR structure on a (4n+3)-dimensional manifold M as a triple (ω1,ω2,ω3) of 1-forms such that the corresponding 2-forms satisfy some algebraic relations. We associate with such a structure an Einstein metric on M and establish relations between quaternionic CR structures, contact pseudo-metric 3-structures and pseudo-Sasakian 3-structures. Homogeneous examples of (para)-quaternionic CR manifolds are given and a reduction construction of non homogeneous (para)-quaternionic CR manifolds is described.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
5
Strony
732-753
Opis fizyczny
Daty
wydano
2004-10-01
online
2004-10-01
Twórcy
Bibliografia
  • [1] D.V. Alekseevsky, V. Cortés: “Classification of pseudo-Riemannian symmetric spaces of quaternionic Kähler type”, Preprint Institut Eli Cartan, Vol. 11, (2004).
  • [2] D.A. Alekseevsky and Y. Kamishima: “Locally pseudo-conformal quaternionic CR structure”, preprint.
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  • [5] D.E. Blair: “Riemannian geometry of contact and symplectic manifolds Contact manifolds”, Birkhäuser, Progress in Math., Vol. 203, (2002).
  • [6] C.P. Boyer, K. Galicki and B.M. Mann: “The geometry and topology of 3-Sasakian manifolds”, Jour. reine ange. Math., Vol. 455, (1994), pp. 183–220.
  • [7] N.J. Hitchin: “The self-duality equations on a Riemannian surface”, Proc. London Math. Soc., Vol. 55, (1987), pp. 59–126.
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  • [9] S. Ishihara: “Quaternion Kählerian manifolds and fibred Riemannian spaces with Sasakian 3-structure”, Kōdai Math. Sem. Rep., Vol. 25, (1973), pp. 321–329.
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  • [11] W. Jelonek: “Positive and negative 3-K-contact structures”, Proc. of A.M.S., Vol. 129, (2000), pp. 247–256. http://dx.doi.org/10.1090/S0002-9939-00-05527-1
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  • [13] T. Kashiwada: “On a contact metric structure”, Math. Z., Vol. 238, (2001), pp. 829–832. http://dx.doi.org/10.1007/s002090100279
  • [14] M. Konishi: “On manifolds with Sasakian 3-structure over quaternionic Kaehler manifolds”, |emphKodai Math. Jour., Vol. 29, (1975), pp. 194–200.
  • [15] S. Kobayashi and K. Nomizu: Foundations of differential geometry I, II, Interscience John Wiley & Sons, New York, 1969.
  • [16] A. Swann: “Aspects symplectiques de la géométrie quaternionique”, C. R. Acad. Sci. Paris, Seria I, Vol. 308, (1989), pp. 225–228.
  • [17] S. Tanno: “Killing vector fields on contact Riemannian manifolds and fibering related to the Hopf fibrations”, |emphTôhoku Math. Jour., Vol. 23, (1971), pp. 313–333.
  • [18] S. Tanno: “Remarks on a triple of K-contact structures”, Tôhoku Math. Jour., Vol. 48, (1996), pp. 519–531.
  • [19] J. Wolf: Spaces of constant curvature, McGraw-Hill, Inc., 1967.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475974
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