Classification of compact complex homogeneous spaces with invariant volumes.
Holomorphic maps of Cartan domains of type four preserving the supports of complex geodesics are characterized, providing, in particular, a new description of holomorphic isometries.
After defining what is meant by a complex spray X on a complex manifold M, we introduce the notion of a spray complex curve associated to X. Several equivalent formulations are derived and we give necessary and sufficient conditions for M to admit spray complex curves for X through each point and in each direction. Refinements of this result are then derived for some special cases, for example when X is the horizontal radial vector field associated to a complex Finsler metric.