Skip to main content
Log in

On structure equations of a three-web Defined by the core of a given left bol three-web

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We give a solution to the problem stated by M. A. Akivis in 1976: Find the structure equations of the 3-web defined by the core of a given Bol 3-web

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. Tolstikhina, G. A., Shelekhov, A. M. “Bol Transformation Quasigroups,” Dokl. Math. 71, No. 2, 201–203 (2005).

    MathSciNet  Google Scholar 

  2. Tolstikhina, G. A., Shelekhov, A. M. “Bol Three-webs Generated by Foliations of Different Dimensions,” Russian Mathematics (Iz. VUZ) 49, No. 5, 52–58 (2005).

    MathSciNet  Google Scholar 

  3. Tolstikhina, G. A., Shelekhov, A. M. “Left Bol Three-webs with IC-Property,” Russian Mathematics (Iz.VUZ) 57, No. 5, 20–28 (2013).

    MathSciNet  Google Scholar 

  4. Tolstikhina, G. A., Shelekhov, A. M. “On the Three-web Associated to the Core of a Left Bol Three-web,” Russian Mathematics (Iz. VUZ) 58, No. 12, 70–74 (2014).

    Google Scholar 

  5. Akivis, M. A., Shelekhov, A. M. Multidimensional Three-webs and Their Applications (Tver StateUniversity, Tver, 2010) [in Russian].

  6. Akivis, M. A. “Differential Geometry of Webs,” in Itogi Nauki i Tekhn. Problemy Geometrii (VINITI, Moscow, 1983), Vol. 15, pp. 187–213.

    MathSciNet  Google Scholar 

  7. Tolstikhina, G. A. “A Generalized Left Bol Three-web Bl(ρ, r, r) as a FactorWeb of a Left BolWeb Bl(r, r, r),” Vesnik Tver Univ. Ser. Prikl. Matem., issue 2(21), No. 21, 117–134 (2011).

    Google Scholar 

  8. Tolstikhina, G. A. “The Conditions for the Coordinate Quasigroup and the Core of a Left Bol Web to BeIsotopic to Each Other,” Izv. Penz. Gos. Pedagog. Univ. Ser. Fiz.-Mat. i Tekhn. Nauki, No. 4(26), 255–262 (2011).

    Google Scholar 

  9. Gegamyan, G. D., Tolstikhina, G. A. “On the Bol Quasigroup Defined by a Group Three-web,” in Proceedingsof the International Conference ‘Education, Science, and Economics at Universities. Integration toInternational Educational Area’, Yerevan, Armenia, September 26–30, 2011 (HΛHPrint, Yerevan, 2012),pp. 86–93.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. M. Shelekhov.

Additional information

Original Russian Text © G.A. Tolstikhina, A.M. Shelekhov, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 8, pp. 75–84.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tolstikhina, G.A., Shelekhov, A.M. On structure equations of a three-web Defined by the core of a given left bol three-web. Russ Math. 59, 62–69 (2015). https://doi.org/10.3103/S1066369X15080071

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X15080071

Keywords

Navigation