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

Masashi Yasumoto, Wayne Rossman

研究成果: Contribution to journalArticle査読

抄録

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.

本文言語英語
ページ(範囲)169-185
ページ数17
ジャーナルOsaka Journal of Mathematics
57
1
出版ステータス出版済み - 1 2020
外部発表はい

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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