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The structure of similarity homogeneous locally compact spaces with an intrinsic metric. II

Abstract

We study locally compact spaces with an intrinsic metric such that the group of metric similarities is transitive and the group of isometries is not transitive. We suggest an algebraic characterization of such spaces.

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References

  1. 1.

    V. N. Berestovskiĭ, “Homogeneous Busemann G-spaces,” Siberian Math. J. 23, 141 (1982) [Sibirsk. Mat. Zh. 23, 3 (1982)].

    MathSciNet  Article  Google Scholar 

  2. 2.

    V. N. Berestovskiĭ, “Structure of homogeneous locally compact spaces with intrinsicmetric,” Siberian.Math. J. 30, 16 (1989) [Sibirsk.Mat. Zh. 30, 23 (1989)].

    Article  Google Scholar 

  3. 3.

    V. N. Berestovskiĭ, “Similarly homogeneous locally complete spaces with an intrinsicmetric,” RussianMath. 48, 1 (2004) [Izv. VUZMat., no. 11, 3 (2004)].

    Google Scholar 

  4. 4.

    V. N. Berestovskiĭ and C. Plaut, “Homogeneous spaces of curvature bounded below,” J. Geom. Anal. 9, 203 (1999).

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    N. Bourbaki, General Topology. Chapters 1–4 (Springer, Berlin, 1998) [éléments de Mathématique. Topologie Générale. Chapitres 1 4 (Springer, Berlin, 2007)].

    MATH  Google Scholar 

  6. 6.

    N. Bourbaki, General Topology. Chapters 5–10 (Springer, Berlin, 1998) [éléments de Mathématique. Topologie Générale. Chapitres 5 10 (Springer, Berlin, 2007)].

    MATH  Google Scholar 

  7. 7.

    H. Busemann, The Geometry of Geodesics (Academic Press, Inc., New York, 1955).

    MATH  Google Scholar 

  8. 8.

    S. Cohn-Vossen, “Existenz kürzesterWege,” CompositioMath. 3, 441 (1936).

    MathSciNet  MATH  Google Scholar 

  9. 9.

    T. Dieck, Transformation Groups (Walter de Gruyter, Berlin, 1987).

    Book  MATH  Google Scholar 

  10. 10.

    R. Engelking, General Topology (Heldermann Verlag, Berlin, 1989).

    MATH  Google Scholar 

  11. 11.

    I. A. Gundyrev, “The structure of similarity homogeneous locally compact spaces with an intrinsic metric,” Siberian Adv. Math. 25, 33 (2015) [Mat. Trudy 17, 132 (2014)].

    MathSciNet  Article  Google Scholar 

  12. 12.

    J.-L. Koszul, Lectures on Groups of Transformations (Tata Inst. Fundam. Research, Bombay, 1965).

    MATH  Google Scholar 

  13. 13.

    E. N. Sosov, “On the finite compactness and completeness of certain mapping spaces with the Busemann metric,” Russian Math. 37, 60 (1993) [Izv. VUZMat., no. 11, 62 (1993)].

    MathSciNet  MATH  Google Scholar 

  14. 14.

    M. Stroppel, Locally Compact Groups (EMS, Zurich, 2006).

    Book  MATH  Google Scholar 

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Correspondence to I. A. Gundyrev.

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Original Russian Text © I.A. Gundyrev, 2015, published in Matematicheskie Trudy, 2015, Vol. 18, No. 1, pp. 15–26.

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Gundyrev, I.A. The structure of similarity homogeneous locally compact spaces with an intrinsic metric. II. Sib. Adv. Math. 26, 182–189 (2016). https://doi.org/10.3103/S1055134416030020

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Keywords

  • similarity homogeneous space
  • group of similarities
  • conformally equivalent space
  • homogeneous space
  • group of isometries
  • intrinsic metric
  • Busemann metric
  • topological groups