A projectively symmetric Finsler space

Symmetric (Riemannian) spaces were introduced and developed by Cartan 1, 2] which led to the discovery of projectively symmetric (Riemannian) spaces by Soós 9]. Recently the theory of symmetric spaces has been extended to Finsler geometry by the present author 5]. The current paper deals with that class of Finsler spaces throughout which their projective curvature tensors possess vanishing covariant derivatives. Following Soós' terminology such spaces are calledprojectively symmetric Finsler spaces. Examples, conditions for a symmetric Finsler space to be projectively symmetric, reduction of various identities, and the discussion of a decomposed projectively symmetric Finsler space form the skeleton of the paper.