The Morse index of minimal products of minimal submanifolds in spheres

作     者：Changping Wang Peng Wang 

作者机构：School of Mathematics and StatisticsFujian Key Laboratory of Mathematical Analysis and ApplicationsFujian Normal UniversityFuzhou 350117China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2023年第66卷第4期

页      面：799-818页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

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

主　　题：minimal product index nullity Clifford minimal submanifold 

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≤ij≤k)(n_(i)+1)(nj+1)(with n=∑n_(j)).