A note on the ultrahyperbolic wave equation in 3+3 dimensions.

This note proves a conjecture of Sparling [Germ of a synthesis: space-time is spinorial, extra dimensions are time-like. Proc R Soc Lond Ser A Math Phys Eng Sci. 2007;463(2083):1665-1679; The Ξ-transform for conformally flat space-time. arXiv:gr-qc/0612006; 2006.], that the ultrahyperbolic wave operator and the Ξ transform on <inline-graphic></inline-graphic> form an exact couple. [ABSTRACT FROM AUTHOR]