Spherically symmetric sprays of isotropic curvature

The classification of sprays with isotropic curvature is a central theme in spray geometry. In this paper, we investigated a class of spherically symmetric sprays—those invariant under spherical rotations. First, we derived a necessary and sufficient condition for such a spray to have isotropic curvature; the condition was a system of differential equations. For the important subclass of projectively affine spherically symmetric sprays, we then obtained the corresponding equivalent system of partial differential equations (PDEs). Furthermore, we constructed several explicit sprays of isotropic curvature.