Rolling construction for anisotropic Delaunay surfaces

Miyuki Koiso, Bennett Palmer

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Anisotropic Delaunay surfaces are surfaces of revolution that have constant anisotropic mean curvature. We show how the generating curves of such surfaces can be obtained as the trace of a point held in a fixed position relative to a curve that is rolled without slipping along a line. This generalizes the Delaunay's classical construction for surfaces of revolution with constant mean curvature. Our result is given as a corollary of a new geometric description of the rolling curve of a general plane curve. Also, we characterize anisotropic Delaunay curves by using their isothermic self-duality.

Original languageEnglish
Pages (from-to)345-378
Number of pages34
JournalPacific Journal of Mathematics
Volume234
Issue number2
DOIs
Publication statusPublished - Feb 1 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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