Skip to main content
SpringerLink
Log in

Eine Verallgemeinerung des Satzes von Holditch

A generalization of the Holditch Theorem

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

The Holditch Theorems for the euclidian plane and the euclidian sphere are generalized for the euclidian space. If we move a hyperbolic linear congruence of linesN along a closed ruled surfaceX, each line ofN generates a closed ruled surfaceY. Some global invariants ofY are linear functions of some global invariants ofX.

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

Similar content being viewed by others

Literatur

  1. Blaschke, W., undH. R. Müller: Ebene Kinematik. München 1956.

  2. Feldmann, U.: Über geschlossene Böschungsflächen. Diss. Darmstadt 1971.

  3. Hacisalihoglu, H. H.: On the pitch of a closed ruled surface. J. Mech. a. Mach. Theory7, 291–305 (1972).

    Google Scholar 

  4. Hoschek, J.: Kinematik. Überbl. Math.1, 193–213 (1968).

    Google Scholar 

  5. Hoschek, J.: Liniengeometrie. Zürich 1971.

  6. Laugwitz, D.: Differentialgeometrie, 2. Aufl. Stuttgart 1968.

  7. Müller, H. R.: Über geschlossene Bewegungsvorgänge. Mh. Math.55, 206–214 (1951).

    Google Scholar 

  8. Müller, H. R.: Sphärische Kinematik. Berlin 1962.

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule, D-6100, Darmstadt, Bundesrepublik Deutschland

    Josef Hoschek

Authors
  1. Josef Hoschek
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Herrn Prof. Dr. K. Strubecker zum 70. Geburtstag gewidmet

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hoschek, J. Eine Verallgemeinerung des Satzes von Holditch. Monatshefte für Mathematik 80, 93–99 (1975). https://doi.org/10.1007/BF01339077

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01339077

Search

Navigation