Skip to main content
Log in

Remarks on Binary Riemannian metrics

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

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.

References

  1. L. V. Ahlfors, «On quasiconformal mappings», Journal d'Analyse Mathématique (Jerusalem), vol. 3 (1953–54), pp. 1–58 and 207–208.

    Article  Google Scholar 

  2. A. D. Alexandrow, «Die innere Geometrie der konvexen Flächen», Berlin, 1955.

  3. S. S. Chern, P. Hartman and A. Wintner, «On isothermic coordinates», Commentarii Mathematici Helvetici, vol. 28 (1954), pp. 301–309.

    Article  MATH  MathSciNet  Google Scholar 

  4. P. Hartman and A. Wintner, «On the curvatures of a surface», American Journal of Mathematics, vol. 75 (1953), pp. 127–141.

    Article  MATH  MathSciNet  Google Scholar 

  5. P. Hartman and A. Wintner, «On the existence of Riemannian manifolds which cannot carry non-constant analytic or harmonic functions in the small», ibid, vol. 75 (1953), pp. 260–276.

    Article  MATH  MathSciNet  Google Scholar 

  6. P. Hartman and A. Wintner, «On uniform Dini conditions in the theory of linear partial differential equations of elliptic type», ibid, vol. 77 (1955), pp. 329–354.

    Article  MATH  MathSciNet  Google Scholar 

  7. T. Levi-Civita, «Forme canoniche dei d s 2 binari con data curvatura totale», Rendiconti della R. Accademia Nazionale dei Lincei, ser. 6, vol. 25 (1937), pp. 197–205.

    MATH  Google Scholar 

  8. L. Lichtenstein, «Zur Theorie der konformen Abbildung. Konforme Abbildung nicht-analytischer singularitätenfreier Flächenstücke auf ebene Gebiete», Bulletin de l'Académie des Sciences de Cracovie, ser. A (1916) pp. 192–217.

  9. H. Petrini, «Les dérivées premières et secondes du potentiel logarithmique», Journal de Mathématiques, ser. 6, vol. 5 (1908), pp. 127–223.

    MathSciNet  Google Scholar 

  10. I. G. Reshetniak, «Isothermic coordinates in manifolds of bounded curvature» (in Russian), Doklady Akad. Nauk U.S.S.R., vol. 64 (1954), pp. 631–633.

    Google Scholar 

  11. H. Weyl, «Die Gibbs'sche Erscheinung in der Theorie der Kugelfunktionen», Rendiconti del Circolo Matematico di Palermo, vol. 29 (1910), pp. 308–323.

    MATH  Google Scholar 

  12. A. Wintner, «On the Hölder restrictions in the theory of partial differential equations», American Journal of Mathematics, vol. 72 (1950), pp. 731–738.

    Article  MATH  MathSciNet  Google Scholar 

  13. A. Wintner, «On isometric surfaces», ibid., vol. 74 (1952), pp. 198–214.

    Article  MATH  MathSciNet  Google Scholar 

  14. A. Wintner, «On the local rôle of the theory of the logarithmic potential in differential geometry», ibid., vol. 75 (1953), pp. 679–690.

    Article  MATH  MathSciNet  Google Scholar 

  15. A. Wintner, «On the local embedding problems in the differential geometry of surfaces», ibid., vol. 77 (1955), pp. 845–852.

    Article  MATH  MathSciNet  Google Scholar 

  16. A. Wintner, “On indefinite binary Riemannian metrics», ibid., vol. 77 (1955), pp. 853–867.

    Article  MATH  MathSciNet  Google Scholar 

Appendix

  1. C. Carathéodory, «Bemerkungen über die Eulerschen Differentialgleichungen der Variationsrechnung», Göttinger Nachrichten, 1931, pp. 40–42.

  2. G. Darboux, «Leçons sur la théorie générale des surfaces», vol. 2, Paris, 1889.

  3. P. Hartman, «On the local uniqueness of geodesics», American Journal of Mathematics, vol. 72 (1950), pp. 723–730.

    Article  MATH  MathSciNet  Google Scholar 

  4. P. Hartman and A. Wintner, «On the third fundamental form of a surface», ibid., vol. 75 (1953), pp. 298–334.

    Article  MATH  MathSciNet  Google Scholar 

  5. P. Hartman and A. Wintner, «Regular binary Pfaffians and non-parabolic partial differential equations», Rendiconti del Circolo Matematico di Palermo, ser. 2, vol. 3 (1954), pp. 347–362.

    Article  MathSciNet  Google Scholar 

  6. E. Kamke, «Differentialgleichungen reeller Funktionen», Leipzig, 1930.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wintner, A. Remarks on Binary Riemannian metrics. Rend. Circ. Mat. Palermo 5, 59–72 (1956). https://doi.org/10.1007/BF02849271

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02849271

Keywords

Navigation