Given a connected simply-connected s-step real nilpotent Lie group G with a left invariant inte-grable 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 pa-per,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.
关键词
连通单连通幂零李群/左不变可积近复结构/幂零复结构/紧致齐性空间
Key words
connected simply-connected nilpotent Lie group/left invariant integrable almost complex st-ru-cture/nilpotent complex structure/compact homogenous space
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