Timelike Christoffel pairs in the split-quaternions
Volume 99 / 2010
Annales Polonici Mathematici 99 (2010), 201-214
MSC: Primary 53A30; Secondary 53C50.
DOI: 10.4064/ap99-2-7
Abstract
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 $\mathbb R^3_2$ to be real or complex isothermic in terms of the existence of integrating factors.
