The Morse index of minimal products of minimal submanifolds in spheres  

作　　者：Changping Wang Peng Wang 

机构地区：[1]School of Mathematics and Statistics,Fujian Key Laboratory of Mathematical Analysis and Applications,Fujian Normal University,Fuzhou 350117,China

出　　处：《Science China Mathematics》2023年第4期799-818,共20页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11831005);supported by National Natural Science Foundation of China(Grant No.11971107)。

摘　　要：Tang and Zhang(2020)and Choe and Hoppe(2018)showed independently that one can produce minimal submanifolds in spheres via the Clifford type minimal product of minimal submanifolds.In this paper,we show that the minimal product is immersed by its first eigenfunctions(of its Laplacian)if and only if the two beginning minimal submanifolds are immersed by their first eigenfunctions.Moreover,we give the estimates of the Morse index and the nullity of the minimal product.In particular,we show that the Clifford minimal submanifold(√n1/nS^(n1).....,√nk/nS^(nk)■S^(n+k-1))has the index(k-1)(n+k+1)and the nullity(k-1)∑_(1≤i<j≤k)(n_(i)+1)(nj+1)(with n=∑n_(j)).

关 键 词：minimal product INDEX NULLITY Clifford minimal submanifold 

分 类 号：O186.1[理学—数学]