Skip to main content
SpringerLink
Log in

Distance geometry of metric arcs II

  • Published:
Archiv der Mathematik 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

Bibliography

  1. W. R. Abel andL. M. Blumenthal, Distance geometry of metric arcs. I. Amer. Math. Monthly64, 1–10 (1957).

    Google Scholar 

  2. C.Pauc, Les méthodes directes en calcul des variations et en géométrie différentielle. Thèses présentées a la Faculté des Sciences de l'Université de Paris. Hermann et Cie, Paris 1941.

  3. L. M. Blumenthal, Theory and applications of distance geometry. The Clarendon Press, Oxford 1953.

    Google Scholar 

  4. L. M. Blumenthal, New characterizations of segments and arcs. Proc. Nat. Acad. Sci. USA29, 107–109 (1943).

    Google Scholar 

  5. A. N. Milgram, Some metric topological invariants. Rep. Math. Colloquium, II. Ser.5, 25–35 (1944).

    Google Scholar 

  6. I. J. Schoenberg, On metric arcs of vanishing Menger curvature. Ann. of Math.41, 715–726 (1940).

    Google Scholar 

  7. A. Marchaud, Sur une propriété topologique intuitive, charactéristique des courbes de Jordan sans point double. Mathematica4, 137–156 (1930).

    Google Scholar 

  8. C. Pauc, Courbure dans les espaces métriques. Rend. R. Accad. Lincei ser. 624, 109–115 (1936).

    Google Scholar 

  9. I. J. Schoenberg, Metric spaces and positive definite functions. Trans. Amer. Math. Soc.44, 522–536 (1938).

    MathSciNet  Google Scholar 

  10. C. Pauc, Sur les possibilités de généralisation d'un théorème de M. Marchaud. Rev. Scientifique2, 104 (1940).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Columbia, Mo.

    William R. Abel & Leonard M. Blumenthal

Authors
  1. William R. Abel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leonard M. Blumenthal
    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

Abel, W.R., Blumenthal, L.M. Distance geometry of metric arcs II. Arch. Math 8, 451–463 (1958). https://doi.org/10.1007/BF01898850

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01898850

Keywords

Search

Navigation