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arXiv · 2004.04447

The Ribaucour families of discrete R-congruences

Thilo Rörig·Gudrun Szewieczek
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Abstract

While a generic smooth Ribaucour sphere congruence admits exactly two envelopes, a discrete R-congruence gives rise to a 2-parameter family of discrete enveloping surfaces. The main purpose of this paper is to gain geometric insights into this ambiguity. In particular, discrete R-congruences that are enveloped by discrete channel surfaces and discrete Legendre maps with one family of spherical curvature lines are discussed.

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Thilo Rörig, Gudrun Szewieczek. 2020-04-09. The Ribaucour families of discrete R-congruences. https://arxiv.org/abs/2004.04447

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