概复齐性空间

<正> 实向量空间V上的一个线性变换I,如果合于I~2=-E(E是么变换),则称I为V上的一个复结构.易知:存在复结构的实向量空间维数必定是偶数,并且可以视为复向量空间.事实上,命

ALMOST COMPLEX HOMOGENEOUS SPACES

The main results of the present paper are:1.If eanonical affine connections of the first type and the second type are identical on a homogeneous Kobayashi manifold, then the transitive analytic automorphie group of the manifold is semisimple.2.In the third and fourth chapter we give the necessary and sufficient conditions for the existence of an invariant complex structure on complex C-spaces of the compact type and the noncompact type.3. On a C-space of the noncompact type, Koszul form is non-degenerate if and only if Jt = tJ, where J.is an invariant complex structure and t is an involutorial automorphism.4. When B is a regular C-subalgebra of G, the C-spaces of the compact type are Hemitian, and Kahlerian, too. At this time Koszul form is negative. So we obtain the results of H. C. Wang 11] and J. L. Koszul for a bounded domain.