Spherically symmetric sprays admit the canonical form G^i = |y|α(r,s) y^i + |y|^2 β(r,s) x^i, with projectively flat ones of isotropic curvature fully classified including explicit zero-curvature cases.
Berwald,Untersuchung der Kr¨ ummung allgemeiner metrischer R¨ aume auf Grund des in ihnen herrschenden Parallelismus, Math
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On Spherically Symmetric Sprays
Spherically symmetric sprays admit the canonical form G^i = |y|α(r,s) y^i + |y|^2 β(r,s) x^i, with projectively flat ones of isotropic curvature fully classified including explicit zero-curvature cases.