THE CLASSIFICATION OF THE COMPLEX STRUCTURES ON ONE CLASS OF SIMPLY CONNECTED COMPACT HOMO GENEOUS SPACES

Let G be a connected compact semisimple Lie group, L its closed subgroup. The necessary and sufficient condition that space G/L has G invariant complex structures(shortened to complex structure in this paper) was first given in Ref. [1]. If G/L has a complex structure, then it is possible that it has infinitely many holomorphic inequivalent complex structures. But, if rank L=rank G, G/L has only many finite