On birecurrent affine motions in a Finsler manifold
Affine motions generated by recurrent and birecurrent vector fields in a non-Riemannian manifold of recurrent curvature were studied by \textit{K. Takano} [Tensor, New Ser. 11, 161-173, 245-253 (1961; Zbl 0099.376)] and by \textit{K. Takano} and \textit{T. Imai} [ibid. 23, 309-313 (1972; Zbl 0259.53019)]. In the present paper the author finds a necessary and sufficient condition for a birecurrent vector field to generate an affine motion in a general Finsler manifold and from this condition deduces the same condition for a recurrent vector field. The author also finds the integrability condition. Finally, the affine motions generated by the above vector fields in some special Finsler manifolds are studied.
scientific article; zbMATH DE number 3921405