Skip to main content
SpringerLink
Log in

Left-invariant hypercontact structures on three-dimensional Lie groups

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We characterize three-dimensional manifolds admitting an almost contact metric 3-structure and completely classify left-invariant hypercontact structures on three-dimensional Lie groups.

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

Access this article

Log in via an institution

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. D.E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Math, vol. 203 (Birkhäuser, Boston, 2001)

    Google Scholar 

  2. G. Calvaruso, Three-dimensional homogeneous almost contact metric structures. J. Geom. Phys. 69, 60–73 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  3. G. Calvaruso, D. Perrone, Contact pseudo-metric manifolds. Diff. Geom. Appl. 28, 615–634 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  4. B. Cappelletti Montano, A. De Nicola, 3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem. J. Geom. Phys. 57, 2509–2520 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. H. Geiges, J. Gonzalo, Contact geometry and complex surfaces. Invent. Math. 121, 147–209 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  6. H. Geiges, C.B. Thomas, Hypercontact manifolds. J. Lond. Math. Soc. 51, 345–352 (1995)

    Article  MathSciNet  Google Scholar 

  7. S. Hohloch, G. Noetzel, D. Salamon, Hypercontact structures and Floer homology. Geom. Topol. 13, 2543–2617 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  8. S. Ianus, R. Mazzocco, G.E. Vilcu, Real lightlike hypersurfaces of paraquaternionic Khler manifolds. Mediterr. J. Math. 3, 581–592 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. T. Kashiwada, On a contact 3-structure. Math. Z. 238, 829–832 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  10. R.C. Kirby, The topology of 4-manifolds, Lecture Notes Mathematics, vol. 1374 (Springer-Verlag, Berlin, 1989)

  11. S. Kaneyuki, M. Konzai, Paracomplex structures and affine symmetric spaces. Tokyo J. Math. 8, 301–318 (1985)

    Google Scholar 

  12. J. Milnor, Curvature of left invariant metrics on Lie groups. Adv. Math. 21, 293–329 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  13. D. Perrone, Hypercontact metric three-manifolds. C. R. Math. Acad. Sci. Soc. R. Can. 24, 97–101 (2002)

    MATH  MathSciNet  Google Scholar 

  14. S. Zamkovoy, Canonical connections on paracontact manifolds. Ann. Glob. Anal. Geom. 36, 37–60 (2009)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors wish to thank the Referee for the valuable suggestions and comments.

Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Fisica “E. De Giorgi”, Università del Salento, Prov. Lecce-Arnesano, 73100, Lecce, Italy

    Giovanni Calvaruso & Antonella Perrone

Authors
  1. Giovanni Calvaruso
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Antonella Perrone
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giovanni Calvaruso.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Calvaruso, G., Perrone, A. Left-invariant hypercontact structures on three-dimensional Lie groups. Period Math Hung 69, 97–108 (2014). https://doi.org/10.1007/s10998-014-0054-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10998-014-0054-z

Keywords

Mathematics Subject Classification

Search

Navigation