The Hermitian connection and the Jacobi fields of a complex Finsler manifold. (Q1608959)

The author re-expresses the Finslerian covariant derivative defined by \textit{S. Kobayashi} [Nagoya Math. J. 57, 153-166 (1975; Zbl 0326.32016)] in terms of the torsion and the curvature two forms of an absolute parallelism defined by himself on a bundle of special linear frames [\textit{A. Spiro}, Asian J. Math. 5, 291-326 (2001; Zbl 1020.53048)]. As an application he writes the equations of the geodesics and of the Jacobi vector fields in terms of Kobayashi's Finslerian connection and of its torsion and curvature.