Semi-discrete linear weingarten surfaces with weierstrass-type representations and their singularities

Masashi Yasumoto, Wayne Rossman

Research output: Contribution to journalArticlepeer-review

Abstract

We establish what semi-discrete linear Weingarten surfaces with Weierstrass-type representations in 3-dimensional Riemannian and Lorentzian spaceforms are, confirming their required properties regarding curvatures and parallel surfaces, and then classify them. We then define and analyze their singularities. In particular, we discuss singularities of (1) semi-discrete surfaces with non-zero constant Gaussian curvature, (2) parallel surfaces of semi-discrete minimal and maximal surfaces, and (3) semi-discrete constant mean curvature 1 surfaces in de Sitter 3-space. We include comparisons with different previously known definitions of such singularities.

Original languageEnglish
Pages (from-to)169-185
Number of pages17
JournalOsaka Journal of Mathematics
Volume57
Issue number1
Publication statusPublished - Jan 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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