Die Öffnungsstrecken der Bahnregelflächen geschlossener räumlicher äquiformer Zwangläufe

Helmut Pottmann

doi:10.1007/BF01559395

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 journal › Article › peer-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 contribution	The aperture distances of the ruled surfaces, generated by closed spatial equiform motions
Original language	German
Pages (from-to)	317-326
Number of pages	10
Journal	Monatshefte für Mathematik
Volume	101
Issue number	4
DOIs	https://doi.org/10.1007/BF01559395
State	Published - Dec 1986
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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title = "Die {\"O}ffnungsstrecken der Bahnregelfl{\"a}chen geschlossener r{\"a}umlicher {\"a}quiformer Zwangl{\"a}ufe",

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.",

author = "Helmut Pottmann",

year = "1986",

month = dec,

doi = "10.1007/BF01559395",

language = "German",

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pages = "317--326",

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AU - Pottmann, Helmut

PY - 1986/12

Y1 - 1986/12

N2 - 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.

AB - 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.

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ER -

Die Öffnungsstrecken der Bahnregelflächen geschlossener räumlicher äquiformer Zwangläufe

Abstract

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