Strict positive definiteness on a product of compact two-point   homogeneous spaces
  We present an explicit characterization for the real, continuous, isotropic and strictly positive definite kernels on a product of compact two-point homogeneous spaces, in the cases in which at least one of the spaces is a sphere of dimension greater than 1 and the other is not a circle. The result complements similar characterizations previously obtained for products of high dimensional spheres. 
V. S. Barbosa and V. A. Menegatto
math.FA