Skip to main content
SpringerLink
Log in

Geodesics of nonholonomic left-invariant intrinsic metrics on the Heisenberg group and isoperimetric curves on the Minkowski plane

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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

References

  1. V. N. Berestovskii, “Homogeneous manifolds with intrinsic metric. I,” Sibirsk. Mat. Zh.,29, No. 6, 17–29 (1988).

    Google Scholar 

  2. V. N. Berestovskii, “Homogeneous spaces with intrinsic metric,” Dokl. Akad. Nauk SSSR,301, No. 2, 268–271 (1988).

    Google Scholar 

  3. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, Mathematical Theory of Optimal Processes [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  4. H. Busemann, The Geometry of Geodesics [Russian translation], Fizmatgiz, Moscow (1962).

    Google Scholar 

  5. K. Leichtweiss, Convex Sets [Russian translation], Nauka, Moscow (1985).

    Google Scholar 

  6. V. N. Berestovskii, “Homogeneous manifolds with intrinsic metric. II,” Sibirsk. Mat. Zh.,30, No. 2, 14–28 (1989).

    Google Scholar 

  7. V. N. Berestovskii, Homogeneous Spaces with Intrinsic Metric [in Russian], Diss. Dokt. Fiz.-Mat. Nauk, Inst. Mat. (Novosibirsk), Novosibirsk (1990).

    Google Scholar 

  8. A. D. Aleksandrov, “über eine Verallgemeinerung der Riemannschen Geometrie,” Schrift. Inst. Math. der Deutschen Acad. Wiss., No. 1, 33–84 (1957).

    Google Scholar 

  9. A. M. Vershik and V. Ya. Gershkovich, “Nonholonomic dynamical systems. Geometry of distributions and variational problems,” in: Sovrem. Probl. Mat. Fund. Naprav. (Itogi Nauki i Tekhniki),16 [in Russian], VINITI, Moscow, 1987, pp. 5–85.

    Google Scholar 

  10. L. S. Kirillova, “Non-Riemmannian metrics and the maximum principle,” Dokl. Akad. Nauk UzSSR, No. 7, 9–11 (1986).

    Google Scholar 

  11. A. M. Vershik and O. A. Granichina, “Reduction of nonholonomic variational problems to isoperimetric problems and connections in principal bundles,” Mat. Zametki,49, No. 5, 37–44 (1991).

    Google Scholar 

  12. R. Montgomery, Shortest Loops with a Fixed Holonomy [Preprint], MSRI (1988).

  13. V. N. Berestovskii, “Submetries of space forms of nonnegative curvature,” Sibirsk. Mat. Zh.,28, No. 4, 44–56 (1987).

    Google Scholar 

  14. Z. Ge, “On a constrained variational problem and the spaces of horizontal paths,” Pacific J. Math.,149, No. 1, 61–94 (1991).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Omsk

    V. N. Berestovskii

Authors
  1. V. N. Berestovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromSibirskii Matematicheskii Zhurnal, Vol. 35, No. 1, pp. 3–11, January–February, 1994.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berestovskii, V.N. Geodesics of nonholonomic left-invariant intrinsic metrics on the Heisenberg group and isoperimetric curves on the Minkowski plane. Sib Math J 35, 1–8 (1994). https://doi.org/10.1007/BF02104943

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02104943

Keywords

Search

Navigation