Quadrics and Scherk towers

S. Fujimori, U. Hertrich-Jeromin, M. Kokubu, M. Umehara, K. Yamada

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We investigate the relation between quadrics and their Christoffel duals on the one hand, and certain zero mean curvature surfaces and their Gauss maps on the other hand. To study the relation between timelike minimal surfaces and the Christoffel duals of 1-sheeted hyperboloids we introduce para-holomorphic elliptic functions. The curves of type change for real isothermic surfaces of mixed causal type turn out to be aligned with the real curvature line net.

Original languageEnglish
Pages (from-to)249-279
Number of pages31
JournalMonatshefte fur Mathematik
Volume186
Issue number2
DOIs
Publication statusPublished - Jun 1 2018

Keywords

  • Causal type
  • Central quadric
  • Christoffel transformation
  • Ellipsoid
  • Hyperboloid
  • Isothermic surface
  • Karcher saddle tower
  • Maximal surface
  • Minimal surface
  • Saddle tower
  • Scherk surface
  • Timelike surface

ASJC Scopus subject areas

  • Mathematics(all)

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    Fujimori, S., Hertrich-Jeromin, U., Kokubu, M., Umehara, M., & Yamada, K. (2018). Quadrics and Scherk towers. Monatshefte fur Mathematik, 186(2), 249-279. https://doi.org/10.1007/s00605-017-1075-5