Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6418875 | Journal of Mathematical Analysis and Applications | 2013 | 9 Pages |
Abstract
In this paper, we prove a classification theorem for stable compact minimal submanifolds of a Riemannian product of an m1-dimensional (m1â¥3) hypersurface M1 in Euclidean space and any Riemannian manifold M2, when the sectional curvature KM1 of M1 satisfies 1m1â1â¤KM1â¤1. In particular, when the ambient space is an m-dimensional (mâ¥3) compact hypersurface M in Euclidean space, if the sectional curvature KM of M satisfies 1m+1â¤KMâ¤1, then we conclude that there exist no stable compact minimal submanifolds in M.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Hang Chen, Xianfeng Wang,