Timelike Christoffel pairs in the split-quaternions

Volume 99 / 2010

M. P. Dussan, M. Magid Annales Polonici Mathematici 99 (2010), 201-214 MSC: Primary 53A30; Secondary 53C50. DOI: 10.4064/ap99-2-7


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.


  • M. P. DussanDepartamento de Matemática - IME
    Universidade de São Paulo
    CEP: 05508-090
    São Paulo S.P., Brazil
  • M. MagidDepartment of Mathematics
    Wellesley College
    Wellesley, MA 02458. U.S.A.

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