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manuscripta mathematica

, Volume 18, Issue 1, pp 15–23 | Cite as

Über die isotropen Strahlensysteme

  • Georg Stamou
Article

Abstract

The main purpose of this paper is to derive integral formulas for the isotropic congruences of the three dimensional Euclidean space. In the last chapter we investigate a special congruence which is derived by a suitable transformation from a given isotropic congruence.

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Literatur

  1. [1]
    EISENHART, L.P.: A treatise on the Differential Geometry of curves and surfaces. Dover, New York 1960.Google Scholar
  2. [2]
    FINIKOW, S.P.: Theorie der Kongruenzen. Akademie Verlag, Berlin 1959.Google Scholar
  3. [3]
    HAACK, W.: Elementare Differentialgeometrie. Birkhäuser, Basel-Stuttgart 1955.Google Scholar
  4. [4]
    HOSCHEK, J.: Liniengeometrie. Zürich 1971.Google Scholar
  5. [5]
    KOMMERELL, K.: Strahlensysteme und Minimalflächen. Math. Ann.70, 143–160 (1911).Google Scholar
  6. [6]
    ROSSINSKI, C.D.: Sur un cas de déformation des congruences isotropes et sur une transformation des surfaces minima qui s'y rattachent. Rend. Palermo59, 82–96 (1935).Google Scholar
  7. [7]
    STAMOU, G.: Strahlensysteme mit gemeinsamem sphärischen Bild. Manuscripta math.15, 329–340 (1975).Google Scholar
  8. [8]
    STEPHANIDIS, N.K.: Beitrag zur Theorie der Strahlensysteme. Habilitationsschrift TU Berlin 1964.Google Scholar
  9. [9]
    STEPHANIDIS, N.K.: Strahlensysteme mit gemeinsamer Mittenhüllfläche. Monatsh. Math.70, 64–73 (1966).Google Scholar
  10. [10]
    STEPHANIDIS, N.K.: Integralformeln in der Liniengeometrie. Math. Nachr.43, 1–9 (1970).Google Scholar
  11. [11]
    VINCENSINI, P.: Congruences isotropes et surfaces minima. CR193, 689 (1931).Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Georg Stamou
    • 1
  1. 1.Mathematisches Institut der UniversitätThessalonikiGriechenland

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