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Mat. Zametki, 2008, Volume 83, Issue 2, Pages 286–304 (Mi mz3812)  

This article is cited in 2 scientific papers (total in 2 papers)

Local Singularities of Chord Sets

L. P. Stunzhas

M. V. Lomonosov Moscow State University

Abstract: In the present paper, we classify the local singularities of chord sets, i.e., of the envelopes of two-parameter families of straight lines connecting pairs of points on two smooth curves in $\mathbb R^3$; we also present geometric criteria for the chord set to have a given local singularity.

Keywords: smooth curves in $\mathbb R^3$, chord set, local singularity, smooth curve, germ of a curve, diffeomorphism, projective invariance

DOI: https://doi.org/10.4213/mzm3812

Full text: PDF file (547 kB)
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English version:
Mathematical Notes, 2008, 83:2, 257–273

Bibliographic databases:

UDC: 514.123.4
Received: 21.11.2006
Revised: 18.04.2007

Citation: L. P. Stunzhas, “Local Singularities of Chord Sets”, Mat. Zametki, 83:2 (2008), 286–304; Math. Notes, 83:2 (2008), 257–273

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm3812
  • http://mi.mathnet.ru/eng/mz/v83/i2/p286

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. M. Zakalyukin, A. N. Kurbatskii, “Envelope Singularities of Families of Planes in Control Theory”, Proc. Steklov Inst. Math., 262 (2008), 66–79  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. Alghanemi A., Giblin P., “On Geometry of the Midlocus Associated to a Smooth Curve in Plane and Space”, Filomat, 32:8 (2018), 2977–2990  crossref  mathscinet  isi  scopus
  • Математические заметки Mathematical Notes
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