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Compact generalized Hopf and cosymplectic solvmanifolds and the Heisenberg groupH(n, 1)

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Abstract

In this paper we obtain a generalized Hopf structure on the total space of certain principal circle bundles over a compact cosympletic manifold. Using this result we give new examples of compact generalized Hopf manifolds. We describe these examples as suspensions with fibre a compact quotient of the generalized Heisenberg groupH(n, 1) by a discrete subgroup and we show an explicit realization of them as compact solvmanifolds.

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References

  1. D. E. Blair,Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics509, Springer-Verlag, Berlin, 1976.

    MATH  Google Scholar 

  2. D. Chinea, M. de León and J. C. Marrero,Topology of cosymplectic manifolds, Journal de Mathématiques Pures et Appliquées72 (1993), 567–591.

    MATH  Google Scholar 

  3. L. A. Cordero, M. Fernández and M. de León,Compact locally conformal Kähler nilmanifolds, Geometriae Dedicata21 (1986), 187–192.

    Article  MATH  MathSciNet  Google Scholar 

  4. L. A. Cordero, M. Fernández and M. de León,Examples of compact almost contact manifolds admitting neither Sasakian nor cosymplectic structures, Atti del Seminario Matematico e Fisico dell’Università di Modena34 (1985-86), 43–54.

    Google Scholar 

  5. Y. Haraguchi,Sur une généralisation des structures de contact, Thèse, Université du Haute Alsace Mulhouse, 1981

    Google Scholar 

  6. G. Hector and U. Hirsch,Introduction to the Geometry of Foliations, Part A,Aspects of Mathematics, Friedr. Vieweg and Sohn, 1981.

  7. S. Kobayashi,Principal fibre bundles with 1-dimensional toroidal group, Tôhoku Mathematical Journal8 (1956), 29–45.

    MATH  Google Scholar 

  8. S. Kobayashi and K. Nomizu,Foundations of Differential Geometry, Vol. I, Interscience, New York-London, 1963.

    MATH  Google Scholar 

  9. J. C. Marrero and E. Padrón,New examples of compact cosymplectic solvmanifolds, preprint.

  10. J. C. Marrero and J. Rocha,Locally conformal Kähler submersions, Geometriae Dedicata52, (1994), 271–289.

    Article  MATH  MathSciNet  Google Scholar 

  11. O’Neill,The fundamental equations of a submersion, The Michigan Mathematical Journal13 (1966), 459–469.

    Article  MATH  MathSciNet  Google Scholar 

  12. S. Tanno,The automorphism groups of almost contact Riemannian manifolds, Tôhoku Mathematical Journal,21 (1969), 21–38.

    MATH  MathSciNet  Google Scholar 

  13. I. Vaisman,On locally conformal almost Kähler manifolds, Israel Journal of Mathematics24 (1976), 338–351.

    MATH  MathSciNet  Google Scholar 

  14. I. Vaisman,Locally conformal Kähler manifolds with parallel Lee form, Rendiconti di Matematica, Roma12 (1979), 263–284.

    MATH  MathSciNet  Google Scholar 

  15. I. Vaisman,Generalized Hopf manifolds, Geometriae, Dedicata13 (1982), 231–255.

    Article  MATH  MathSciNet  Google Scholar 

  16. J. A. Wolf,Spaces of Constant Curvature, 5th ed., Publish or Perish, Inc., Wilmington, Delaware, 1984.

    Google Scholar 

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Authors and Affiliations

  1. Depto. Matemática Fundamental, Universidad de La Laguna, Tenerife, Canary Islands, Spain

    Juan Carlos Marrero & Edith Padrón

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  1. Juan Carlos Marrero
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  2. Edith Padrón
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Correspondence to Juan Carlos Marrero.

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Marrero, J.C., Padrón, E. Compact generalized Hopf and cosymplectic solvmanifolds and the Heisenberg groupH(n, 1). Isr. J. Math. 101, 189–204 (1997). https://doi.org/10.1007/BF02760929

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  • DOI: https://doi.org/10.1007/BF02760929

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