Area-minimizing Cones over Stiefel Manifolds  

Stiefel流形上的面积最小锥

作　　者：JIAO Xiaoxiang XIN Jialin CUI Hongbin 焦晓祥;辛嘉麟;崔洪斌(中国科学院大学数学科学学院,北京100049;五邑大学数学与计算科学学院,广东江门529020;中国科学技术大学数学科学学院,安徽合肥230026)

机构地区：[1]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing,100049,P.R.China [2]School of Mathematics and Computational Science,Wuyi University,Jiangmen,Guangdong,529020,P.R.China [3]School of Mathematical Sciences,University of Science and Technology of China,Hefei,Anhui,230026,P.R.China

出　　处：《数学进展》2024年第5期929-952,共24页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.11871450);Project of Stable Support for Youth Team in Basic Research Field,CAS(No.YSBR-001).

摘　　要：We study the area-minimization property of the cones over Stiefel manifolds V_(m)(F^(n))(F=R,C or H)and their products,where the Stiefel manifolds are embedded into the unit sphere of Euclidean space in a standard way.We will show that these cones are areaminimizing if the dimension is at least 7,using the Curvature Criterion of[Mem.Amer.Math.Soc.,1991,91(446):vi+111 pp.].This extends the results of corresponding references,where the cones over products of Grassmann manifolds were considered.本文研究Stiefel流形V_(m)(F^(n))(F=R,C或H)以及它们的乘积生成的锥,其中Stiefel流形以典则的方式嵌入到欧氏空间的单位球中.用[Mem.Amer.Math.Soc.,1991,91(446):vi+111pp.]中的曲率判别法证明了当这些锥维数≥7时一定是面积最小的.这拓展了相关文献中关于Grassmann流形的结果.

关 键 词：area-minimizing cone calibrated geometry 

分 类 号：O186.1[理学—数学]