Skip to main content
SpringerLink
Log in

Geodesic uniqueness in the whole of some generally recurrent Riemannian spaces

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

In this paper, we present a detailed proof of two theorems of geodesic uniqueness in the whole of compact, in some sense generally recurrent, Riemannian spaces with a positively defined metric. Our studies are based on the H. Hopf theorem.

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. L. P. Eisenhart, Riemannian Geometry, Princeton Univ. Press (1962).

  2. K. Jano and S. Bochner, Curvature and Betti Numbers, Princeton Univ. Press (1953).

  3. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Interscience Publishers, London (1963).

    MATH  Google Scholar 

  4. N. S. Sinyukov, Geodesic Mappings of Riemannian Spaces [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  5. H. N. Sinyukova, “On geodesic mappings of some special Riemannian spaces,” Mat. Zametki, 30, No. 6, 889–894 (1981).

    MathSciNet  Google Scholar 

  6. S. E. Stepanov, “Theorems of disappearance in affine, Riemannian and Lorentz geometries,” Fundam. Prikl. Mat., 11, No. 1, 35–84 (2005).

    MATH  Google Scholar 

  7. G. Vránceanu, “Propriet´ati globale ale spaliilor bui Riemann cu conexiane abina constanta,” Stud. Cerc. Mat., 14, No. 1, 7–22 (1963).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. South-Ukrainian National Pedagogical University, Odessa, Ukraine

    H. N. Sinyukova

Authors
  1. H. N. Sinyukova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. N. Sinyukova.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 2, pp. 93–101, 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sinyukova, H.N. Geodesic uniqueness in the whole of some generally recurrent Riemannian spaces. J Math Sci 177, 710–715 (2011). https://doi.org/10.1007/s10958-011-0500-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-011-0500-x

Keywords

Search

Navigation