Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space

Atsufumi Honda, Miyuki Koiso, Kentaro Saji

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Fold singular points play important roles in the theory of maximal surfaces. For example, if a maximal surface admits fold singular points, it can be extended to a timelike minimal surface analytically. Moreover, there is a duality between conelike singular points and folds. In this paper, we investigate fold singular points on spacelike surfaces with non-zero constant mean curvature (spacelike CMC surfaces). We prove that spacelike CMC surfaces do not admit fold singular points. Moreover, we show that the singular point set of any conjugate CMC surface of a spacelike Delaunay surface with conelike singular points consists of (2, 5)-cuspidal edges.

Original languageEnglish
Pages (from-to)245-267
Number of pages23
JournalHokkaido Mathematical Journal
Volume47
Issue number2
Publication statusPublished - Jan 1 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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