Die Öffnungsstrecken der Bahnregelflächen geschlossener räumlicher äquiformer Zwangläufe

Translated title of the contribution: The aperture distances of the ruled surfaces, generated by closed spatial equiform motions

Helmut Pottmann*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let the orientated line {Mathematical expression} of the three-dimensional moving space Σ, trace out a closed ruled surface {Mathematical expression} in the fixed space Σ′ and let us consider an integral invariant {Mathematical expression} the aperture distance of an orthogonal trajectory of its generators. Then the locus of lines {Mathematical expression} with a given σ is a cyclic quadratic complex, which reduces to a linear complex in the case σ=0. Furthermore in this paper some line-geometric Holditch-theorems due to S. Hentschke [6], L. Hering [7] and J. Hoschek [9], are generalized.

Translated title of the contributionThe aperture distances of the ruled surfaces, generated by closed spatial equiform motions
Original languageGerman
Pages (from-to)317-326
Number of pages10
JournalMonatshefte für Mathematik
Volume101
Issue number4
DOIs
StatePublished - Dec 1 1986

ASJC Scopus subject areas

  • Mathematics(all)

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