@article{59e139d421b04820a1236e074754792c,
title = "Quadrics and Scherk towers",
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.",
keywords = "Causal type, Central quadric, Christoffel transformation, Ellipsoid, Hyperboloid, Isothermic surface, Karcher saddle tower, Maximal surface, Minimal surface, Saddle tower, Scherk surface, Timelike surface",
author = "S. Fujimori and U. Hertrich-Jeromin and M. Kokubu and M. Umehara and K. Yamada",
note = "Funding Information: Acknowledgements Open access funding provided by Austrian Science Fund (FWF). This work would not have been possible without the valuable and enjoyable discussions with B Springborn and E Tjaden about the subject more than a decade ago; further we would like to thank A Honda, M Pember for fruitful more recent discussions around the subject. This work has been partially supported by the Austrian Science Fund (FWF) and the Japan Society for the Promotion of Science (JSPS) through the FWF/JSPS Joint Project grant I1671-N26 “Transformations and Singularities”. Furthermore, we gratefully acknowledge partial support from JSPS through personal grants: Fujimori (B) 25800047; Umehara (A) 26247005; Yamada (C) 26400066; as well as from the Wesco Scientific Promotion Foundation: Fujimori. Publisher Copyright: {\textcopyright} 2017, The Author(s).",
year = "2018",
month = jun,
day = "1",
doi = "10.1007/s00605-017-1075-5",
language = "English",
volume = "186",
pages = "249--279",
journal = "Monatshefte fur Mathematik",
issn = "0026-9255",
publisher = "Springer Wien",
number = "2",
}