Skip to main content
SpringerLink
Log in

On a problem of Chern-Akivis-Shelekhov on hexagonal three-webs

  • Research Papers
  • Published:
aequationes mathematicae Aims and scope Submit manuscript

Summary

In the following we discuss the infinitesimal theory of analytic multidimensional hexagonal three-webs. It is known that the structure of any such three-web in a neighborhood of an arbitrary point is uniquely determined by four tensor values at the given point. We prove that three of them are sufficient and we analyze the corresponding integrability conditions.

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. Chern, S. S.,Eine Invariantentheorie der Dreigewebe aus r-dimensionalen Mannigfaltigkeiten im R 2r . Abh. Math. Sem. Univ. Hamburg11 (1936), 333–358.

    Google Scholar 

  2. Akivis, M. A.,Differential geometry of 3-webs. VINITI Akad. Nauk SSSR: Problems in geometry15 (1983), 187–213.

    Google Scholar 

  3. Kikkawa, M.,Canonical connections of homogeneous Lie loops and 3-webs. Mem. Fac. Sci. Shimane Univ.19 (1985), 37–55.

    Google Scholar 

  4. Shelekhov, A. M.,On differential-geometric objects of high order corresponding to a multidimensional three-web. VINITI Akad. Nauk SSSR: Problems in geometry19 (1987), 101–154.

    Google Scholar 

  5. Mikheev, P. O. andSabinin, L. V.,Smooth quasigroups and geometry. VINITI Akad. Nauk SSSR: Problems in geometry20 (1988), 75–110.

    Google Scholar 

  6. Mikheev, P. O. andSabinin, L. V. Quasigroups and differential geometry. InQuasigroups and loops: Theory and applications. Heldermann Verlag, Berlin, 1990, pp. 357–430.

    Google Scholar 

  7. Goldberg, V. V.,Differentiable quasigroups and webs. InQuasigroups and loops: Theory and applications. Heldermann Verlag, Berlin, 1990, pp. 263–312.

    Google Scholar 

  8. Akivis, M. A. andShelekhov, A. M.,Geometry and algebra of multidimensional 3-webs. Kluwer Academic Publ., Doordrecht—Boston—London, 1992.

    Google Scholar 

  9. Akivis, M. A.,On three-webs of multidimensional surfaces. VINITI Akad. Nauk SSSR: Trudy Geom. Sem.2 (1969), 7–31.

    Google Scholar 

  10. Shelekhov, M. A.,The g-structure associated with a multidimensional hexagonal 3-web is closed. J. Geom.35 (1989), 167–176.

    Article  Google Scholar 

  11. Chern, S. S.,Web geometry. Bull. Amer. Math. Soc.6 (1987), 1–8.

    Google Scholar 

  12. Mikheev, P. O.,On 4-order alternators of the three-web associated with an analytic loop. Izv. Vyssh. Uchebn. Zaved. Mat.6 (1991), 36–38.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of mathematics, Friendship of Nations University, M.-Maklaya 6, 117198, Moscow, Russia

    P. O. Mikheev

Authors
  1. P. O. Mikheev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mikheev, P.O. On a problem of Chern-Akivis-Shelekhov on hexagonal three-webs. Aeq. Math. 51, 1–11 (1996). https://doi.org/10.1007/BF01831136

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01831136

AMS (1991) subject classification

Search

Navigation