Projective complex Finsler metrics

In this paper we obtain the conditions in which two complex Finsler metrics are projective, i.e. have the same geodesics as point sets. Two important classes of such metrics are submitted to our attention: conformal projective and weakly projective complex Finsler spaces. For each of them we study the transformations of the canonical connection. We pay attention for local projectivity with a pure Hermitian or Kähler space. 2000 Mathematics Subject Classification: 53C60, 53B40.