Skip to main content
SpringerLink
Log in

On conformal subriemannian fundamental graded Lie algebras and Cartan connections

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

Abstract

Under some condition we classify the prolongations of conformal subriemannian fundamental graded Lie algebras. Also we show the existence of a normal Cartan connection associated with a bracket generating regular conformal subriemannian manifold.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Bourbaki, Groupes et algèbres de Lie (Hermann, Paris, 1968), Chaps. 4–6.

    MATH  Google Scholar 

  2. J.-H. Cheng, Trans. Amer.Math. Soc. 302(2), 467 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Čap and J. Slavak, Parabolic Geometries I, Background and General Theory (Am. Math. Soc., Providence, R.I., 2009).

    MATH  Google Scholar 

  4. E. Falbel and J. M. Veloso, Forum Mathematicum 10(4), 453 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  5. S. Gomyo, Algebras, Groups Geometries 13, 431 (1996).

    MATH  MathSciNet  Google Scholar 

  6. T. Morimoto, HokkaidoMath. J. 22, 263 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  7. T. Morimoto, Differ. Geometry Appl. 26, 75 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  8. T. Morimoto and N. Tanaka, J.Math. Kyoto Univ. 10(2), 207 (1970).

    MATH  MathSciNet  Google Scholar 

  9. A. L. Onishchik and V. L. Vinberg, Lie Groups and Lie Algebras III: Structure of Lie Groups and Lie Algebras (Springer, New York, 1994).

    Book  MATH  Google Scholar 

  10. N. Tanaka, J.Math. Kyoto Univ. 10, 1 (1970).

    MATH  MathSciNet  Google Scholar 

  11. H. Wakakuwa, Holonomy Group, Publications of the Study Group of Geometry 6 (1971).

  12. G. Warner, Harmonic Analysis on Semi-Simple Lie Groups (Springer, New York, 1972), Vol. 1.

    Book  Google Scholar 

  13. K. Yamaguchi, Adv. Stud. PureMath. 22, 413 (1993).

    Google Scholar 

  14. T. Yatsui, HokkaidoMath. J. 17, 333 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  15. I. Yokota, Exceptional Lie Groups, ArXiv:0902.0431v1 [math.DG] (2009).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tomoaki Yatsui, 1-9-2 Masakae, Otaru, 047-0003, Japan

    Tomoaki Yatsui

Authors
  1. Tomoaki Yatsui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tomoaki Yatsui.

Additional information

Submitted by V. V. Lychagin

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yatsui, T. On conformal subriemannian fundamental graded Lie algebras and Cartan connections. Lobachevskii J Math 36, 169–177 (2015). https://doi.org/10.1134/S1995080215020183

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080215020183

Keywords and phrases

Search

Navigation