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

作　　者：杜材煜 王瑜 DU Cai-yu;WANG Yu(School of Mathematics and Statistics,Sichuan University of Science and Engineering,Zigong 643000,China)

机构地区：[1]四川轻化工大学数学与统计学院,四川自贡643000

出　　处：《兰州理工大学学报》2024年第3期167-172,共6页Journal of Lanzhou University of Technology

基　　金：四川轻化工大学人才引进项目(2020RC26)的资助

摘　　要：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.

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 

分 类 号：O186.12[理学—数学]