Advertisement

Rendiconti del Circolo Matematico di Palermo

, Volume 37, Issue 1, pp 8–17 | Cite as

On the rectilinear congruences of Lorentz manifold [R 3,(+,+,−)] establishing a mapping between its focal surfaces, preserving the mean curvatures

  • B. J. Papantoniou
Article
  • 18 Downloads

Abstract

This paper contains four paragraphs. In the first paragraph we consider a hyperbolic rectilinear congruence of the Lorentz manifold [R 3,(+,+,−)] the linear element of the system of three partial differential equations in which is reduced the problem of determing the rectilinear congruences of the Lorentz manifold (R 3,g) the straight lines of which establish a mapping between their focal surfaces which preserves the mean curvatures (locally). In the second paragraph under the assumptions (2.1) we reduce this system equivalently to the system (2.7) and (2.8) and exspress the theorem 2.1. In the third paragraph under the assumptions (3.1) we succeed to give the solution of the system and exspress the theorem 3.1. In the fourth paragraph we suppose that the linear element of the spherical representation in known (assumption 4.2) and give the class of rectilinear congruences the semidistance of which is given by (4.13) with the mentioned property and express the theorem 4.1.

Keywords

Partial Differential Equation Arbitrary Function Normal Bundle Technology Department Developable Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bianchi L.,Lezioni di Geometria differentiale, Zanichelli, Bologna (1927).Google Scholar
  2. [2]
    Eisenhart L.,Differential geometry, Dover publications, INC N.Y. (1960).MATHGoogle Scholar
  3. [3]
    Pylarinos O.,Sur les à courbure moyenne constante applicable sur de surface de revolution, Annali di Matematica pura et applicata,59, (1962) 319–350.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Papantoniou B.,On the surfaces of Lorentz manifold whose normal bundles have special properties, Annali di Matematica pura ed applicata (IV), Vol. CXXXV, (1983) 319–328.CrossRefMathSciNetGoogle Scholar
  5. [5]
    Tsagas Gr.,Classification of rectilinear congruences with special properties, Tensor N. S26 (1972) 271–276.MATHMathSciNetGoogle Scholar
  6. [6]
    Tsagas Gr., Papantoniou B.,On the rectilinear congruences establishing a mapping between its focal surfaces which preserves the Gauss curvature, Annali di Matematica pura ed applicata (IV), Vol. CXXXI, (1982), 255–264.CrossRefMathSciNetGoogle Scholar
  7. [7]
    Tsagas Gr., Papantoniou B.,Special class of rectilinear congruences, Tensor N. S43 (1986), 213–216.MATHMathSciNetGoogle Scholar

Copyright information

© Springer 1988

Authors and Affiliations

  • B. J. Papantoniou
    • 1
  1. 1.School of Technology Department of Physics and Mathematics Mathematics divisionUniversity of ThessalonikiThessalonikiGreece

Personalised recommendations