Discrete channel surfaces

Hertrich-Jeromin, Udo; Rossman, Wayne; Szewieczek, Gudrun

doi:10.1007/s00209-019-02389-4

Record link:

https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:3-7875
http://hdl.handle.net/20.500.12708/753

Title:

Citation:

Hertrich-Jeromin, U., Rossman, W., & Szewieczek, G. (2020). Discrete channel surfaces. Mathematische Zeitschrift, 294(1–2), 747–767. https://doi.org/10.1007/s00209-019-02389-4

Publisher DOI:

10.1007/s00209-019-02389-4

CatalogPlus:

AC15533572

Publication Type:

Article - Original Research Article

Language:

English

Authors:

Hertrich-Jeromin, Udo
Rossman, Wayne
Szewieczek, Gudrun

Organisational Unit:

E104-03 - Forschungsbereich Differentialgeometrie und geometrische Strukturen

Journal:

Mathematische Zeitschrift

ISSN:

0025-5874

Date (published):

Feb-2020

Number of Pages:

Publisher:

Springer

Peer reviewed:

Yes

Keywords:

Channel surface; Dupin cyclide; Lie sphere geometry; Discrete Legendre map; Lie cyclide; Blending surface; Vessiot’s Theorem; Discrete isothermic net; Ribaucour transformation

Abstract:

We present a definition of discrete channel surfaces in Lie sphere geometry, which reflects several properties for smooth channel surfaces. Various sets of data, defined at vertices, on edges or on faces, are associated with a discrete channel surface that may be used to reconstruct the underlying particular discrete Legendre map. As an application we investigate isothermic discrete channel surfaces and prove a discrete version of Vessiot’s Theorem.

License:

CC BY 4.0