Ribaucour coordinates

Burstall, Francis; Hertrich-Jeromin, Udo; Lara Miro, Maria

doi:10.1007/s13366-018-0391-9

Record link:

https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:3-5206
http://hdl.handle.net/20.500.12708/570

Title:

Citation:

Burstall, F., Hertrich-Jeromin, U., & Lara Miro, M. (2019). Ribaucour coordinates. Beitraege Zur Algebra Und Geometrie, 60, 39–55. https://doi.org/10.1007/s13366-018-0391-9

Publisher DOI:

10.1007/s13366-018-0391-9

CatalogPlus:

AC15324298

Publication Type:

Article - Original Research Article

Language:

English

Authors:

Burstall, Francis
Hertrich-Jeromin, Udo
Lara Miro, Maria

Organisational Unit:

E104-03 - Forschungsbereich Differentialgeometrie und geometrische Strukturen

Journal:

Beitraege zur Algebra und Geometrie

ISSN:

0138-4821

Date (published):

2019

Number of Pages:

Publisher:

Springer

Peer reviewed:

Yes

Keywords:

Channel surface; Canal surface; Semi-discrete surface; Curvature line net; Discrete principal net; Circular net; Ribaucour transformation; Ribaucour coordinates

Abstract:

We discuss results for the Ribaucour transformation of curves or of higher dimensional smooth and discrete submanifolds. In particular, a result for the reduction of the ambient dimension of a submanifold is proved and the notion of Ribaucour coordinates is derived using a Bianchi permutability theorem. Further, we discuss smoothing of semi-discrete curvature line nets and an interpolation by Ribaucour transformations.

License:

CC BY 4.0