NONEXISTENCE OF PETROV TYPE-III SPACE-TIMES ON WHICH WEYL NEUTRINO EQUATION OR MAXWELL EQUATIONS SATISFY HUYGENS PRINCIPLE

Extending previous results we show that there are no Petrov type III s pace-times on which either the Weyl neutrino equation or Maxwell's equ ations satisfy Huygens' principle. We prove the result by using Maple' s NPspinor package to convert the five-index necessary condition obtai ned by Alvarez and Wunsch to dyad form. The integrability conditions o f the problem lead to a system of polynomial equations, We then apply Maple's grobner package to show that this system has no admissible sol utions.