On complex Douglas spaces (Q1947591)

A projective change between two complex Finsler manifolds gives rise to projective curvature invariants, three of Douglas type and two of Weyl type. The vanishing of all projective curvature invariants of Douglas type defines complex Douglas spaces while the projective invariant of Weyl type characterizes complex Berwald spaces. The present paper describes several relationships between complex Douglas spaces and other classes of complex Finsler manifolds using the equations of a complex geodesic curve. The results are applied to complex Randers spaces.