Skip to main content
Log in

On Harmonic and C-Harmonic 1-Differentiable Forms on Sasakian Manifolds

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we firstly extend some classical operators on Sasakian manifolds acting to 1-differentiable forms on Sasakian manifolds. Next in a similar manner with the study of C-harmonic forms, we define and extend such a study for the case of 1-differentiable forms on Sasakian manifolds.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Blair, D.E.: Riemannian Geometry of Contact and Symplectic Manifolds. Progress in Mathematics, vol. 203. Birkhäuser Boston, Inc., Boston (2002)

  2. Bott, R., Tu, L.W.: Differential Forms in Algebraic Topology, Graduate Text in Mathematics, vol. 82. Springer, Berlin (1982)

  3. Boyer, C.P., Galicki,K.: Sasakian geometry, Oxford Mathematical Monographs. Oxford University Press, Oxford (2008)

  4. Chinea D., Marrero J.C., de Leon M.: A Canonical Differential Complex for Jacobi Manifolds. Michigan Math. J. 45, 547–579 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  5. Flato, M., Lichnerowicz, A., Sternheimer, D.: Déformations 1-différentiables des algèbres de Lie attachées à à une variété symplectique ou de contact. Compos. Math. 31(1), 47–82 (1975)

    Google Scholar 

  6. Fujitani T.: Complex-valued differential forms on normal contact Riemannian manifolds. Tôhoku Math. J. 18, 349–361 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  7. Ida, C., Mercheşan, S.: Some remarks about 1-differentiable cohomology of Sasakian manifolds. In: Proceedings of the 12-th Conference on Applied Mathematics APLIMAT, 5–7 February 2013, Bratislava. Paper No. 33, 11 pp. Slovak University of Technology, Publishing House of STU, Bratislava, ISBN 978-80-227-3865-1. Aplimat-J. Appl. Math. 2013 (To appear)

  8. Kobayashi, S., Nomizu, K.: Foundations of differential geometry. In: Interscience Tracts in Pure and Applied Mathematics, vol. I. Interscience Publ., London (1969)

  9. de León M., Marrero J.C., Padrón E.: Lichnerowicz-Jacobi cohomology. J. Phys. A: Math. Gen. 30, 6029–6055 (1997)

    Article  MATH  Google Scholar 

  10. de León, M., López, B., Marrero, J.C., Padrón, E.: Lichnerowicz-Jacobi cohomology and homology of Jacobi manifolds: modular class and duality. arXiv: math/9910079v1 [math.DG] (1999)

  11. de León M., López B., Marrero J.C., Padrón E.: On the computation of the Lichnerowicz-Jacobi cohomology. J. Geom. Phys. 44, 507–522 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Lichnerowicz, A.: Cohomologie 1-differentiable des algébres de Lie attachées a une variété symplectique ou de contact. J. Math. pures et Appl. 53, 459–484 (1974)

    Google Scholar 

  13. Lichnerowicz A.: Les variétés de Poisson et leurs algébres de Lie associées. J. Diff. Geom. 12, 253–300 (1977)

    MATH  MathSciNet  Google Scholar 

  14. Lichnerowicz A.: Les variétés de Jacobi et leurs algébres de Lie associées. J. Math. pures et Appl. 57, 453–488 (1978)

    MATH  MathSciNet  Google Scholar 

  15. Ogawa Y.: On C-harmonic forms in a compact Sasakian space. Tôhoku Math. J. 19, 267–296 (1967)

    Article  MATH  Google Scholar 

  16. Pitis, G.: Contact Geometry: Sasaki manifolds, Kenmotsu manifolds (2013, unpublished)

  17. Reeb G.: Sur certaines propriétés topologiques des trajectoires des systémes dynamiques. Mémoires Acad. Roy. Belgique 27, 1–62 (1952)

    MathSciNet  Google Scholar 

  18. Tachibana S.: On harmonic tensors in compact Sasakian spaces. Tôhoku Math. J. 17, 271–284 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  19. Tachibana S.: On a decomposition of C-harmonic forms in a compact Sasakian space. Tôhoku Math. J. 19, 198–212 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  20. Vaisman, I.: Cohomology and differential forms. M. Dekker Publishing House, New York (1973)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Cristian Ida.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ida, C., Mercheşan, S. On Harmonic and C-Harmonic 1-Differentiable Forms on Sasakian Manifolds. Mediterr. J. Math. 11, 155–171 (2014). https://doi.org/10.1007/s00009-013-0314-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00009-013-0314-9

Mathematics Subject Classification (2010)

Keywords

Navigation