We characterize the Christoffel pairs of timelike isothermic surfaces in the four-dimensional split-quaternions. When restricting the receiving space to the three-dimensional imaginary split-quaternions, we establish an equivalent condition for a timelike surface in ℝ³₂ to be real or complex isothermic in terms of the existence of integrating factors.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-2-7,
author = {M. P. Dussan and M. Magid},
title = {Timelike Christoffel pairs in the split-quaternions},
journal = {Annales Polonici Mathematici},
volume = {98},
year = {2010},
pages = {201-214},
zbl = {1217.53012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-2-7}
}
M. P. Dussan; M. Magid. Timelike Christoffel pairs in the split-quaternions. Annales Polonici Mathematici, Tome 98 (2010) pp. 201-214. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-2-7/