紧致齐性空间G/T上复结构的若干性质

Some properties of complex structures on compact homogenous space G/T

设G为连通单连通s阶实幂零李群,且其上有左不变可积近复结构J,T为李群G的最大秩的格;考虑紧致齐性空间G/T上是否有幂零复结构;运用归纳法证明了复结构J可诱导出紧致齐性空间G/T的可积复结构J且是幂零的.

Given a connected simply-connected s-step real nilpotent Lie group G with a left invariant integrable almost complex structure J and a lattice T of maximal rank of the Lie group G,the existence of a nilpotent complex structure on the compact homogeneous space G/T is considered.It is shown in this paper,through the use of inductive methods,that the complex structure J can induce an integrable complex structure J~on the compact homogeneous space G/T,and that J is nilpotent.