Quadrics and Scherk towers

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

Research output: Contribution to journalArticle

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)1-31
Number of pages31
JournalMonatshefte fur Mathematik
DOIs
Publication statusAccepted/In press - Jul 3 2017

Fingerprint

Quadric
Gauss Map
Elliptic function
Minimal surface
Mean Curvature
Analytic function
Curvature
Curve
Line
Zero

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)

Cite this

Fujimori, S., Hertrich-Jeromin, U., Kokubu, M., Umehara, M., & Yamada, K. (Accepted/In press). Quadrics and Scherk towers. Monatshefte fur Mathematik, 1-31. https://doi.org/10.1007/s00605-017-1075-5

Quadrics and Scherk towers. / Fujimori, Shoichi; Hertrich-Jeromin, U.; Kokubu, M.; Umehara, M.; Yamada, K.

In: Monatshefte fur Mathematik, 03.07.2017, p. 1-31.

Research output: Contribution to journalArticle

Fujimori, S, Hertrich-Jeromin, U, Kokubu, M, Umehara, M & Yamada, K 2017, 'Quadrics and Scherk towers', Monatshefte fur Mathematik, pp. 1-31. https://doi.org/10.1007/s00605-017-1075-5
Fujimori S, Hertrich-Jeromin U, Kokubu M, Umehara M, Yamada K. Quadrics and Scherk towers. Monatshefte fur Mathematik. 2017 Jul 3;1-31. https://doi.org/10.1007/s00605-017-1075-5
Fujimori, Shoichi ; Hertrich-Jeromin, U. ; Kokubu, M. ; Umehara, M. ; Yamada, K. / Quadrics and Scherk towers. In: Monatshefte fur Mathematik. 2017 ; pp. 1-31.
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