Huygens operators on product manifolds
Norio Shimakura · Tohoku Mathematical Journal · 2003
Based on two equalities for power series which are equivalent to the Tedone formulas, the elementary solution to the wave operator on the product of $k$ Riemannian manifolds is represented as a composition, with respect to the time variable, of $k$ elementary solutions to wave operators on factor manifolds. As a consequence, one has an infinite number of non-trivial momentary Huygens operators. For example, wave operators on the product of an odd numer of odd dimensional manifolds with constant curvature are revealed to be momentary Huygens operators for an appropriate choice of coefficients of the 0-th order terms.