四元Stiefel流形上的不变Einstein-Randers度量  

Invariant Einstein-Randers Metrics on Quaternionic Stiefel Manifolds

作　　者：黎小胜 陈慧斌 Li Xiaosheng;Chen Huibin(School of Mathematics and Statistics,Xinyang Normal University,Xinyang 464000,China;School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China)

机构地区：[1]信阳师范学院数学与统计学院,河南信阳464000 [2]南京师范大学数学科学学院,江苏南京210023

出　　处：《南开大学学报（自然科学版）》2023年第2期1-6,共6页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported by NSFC(11547122, 11571182, 11901300);NSFC Tianyuan Visiting Scholar Program in Mathematics(12226339);The Key Research Project of Henan Higher Education Institutions(China)(22A110021);Nanhu Scholars Program for Young Scholars of XYNU。

摘　　要：主要考虑H^(n)上具有标准正交化的p-框架的四元Stiefel流形V_(p)H^(n)上的不变Einstein-Randers度量,这里的V_(p)H^(n)微分同胚于齐性空间Sp(n)/Sp(n-p).证明对任何的2≤p≤(3/4)n,Sp(n)/Sp(n-p)上至少存在两族Sp(n)-不变的Einstein-Randers度量;同时,Sp(3)/Sp(1)以及Sp(4)/Sp(2)上至少存在八族不变Einstein-Randers度量.The invariant Einstein-Randers metrics on the quaternionic Stiefel manifold V_(p)H^(n) of every orthonormal p-frame in H^(n) are considered, V_(p)H^(n) is diffeomorphic to the homogeneous space Sp(n)/Sp(n-p).It's proved that there are at least two families of Sp(n)-invariant Einstein-Randers metrics on Sp(n)/Sp(n-p) for any 2≤p≤(3/4)n and eight families of invariant Einstein-Randers metrics on Sp(3)/Sp(1) and Sp(4)/Sp(2).

关 键 词：Einstein-Randers度量 FINSLER流形 四元Stiefel流形 

分 类 号：O175.29[理学—数学]