The Multiplicity of Eigenvalues of the Hodge Laplacian on 5-Dimensional Compact Manifolds

被引：0
作者：
Megan E. Gier
Peter D. Hislop
机构：
[1] Grove City College,Department of Mathematics
[2] University of Kentucky,Department of Mathematics
来源：
The Journal of Geometric Analysis | 2016年 / 26卷
关键词：
Hodge Laplacian; Eigenvalues; Multiplicity ; Forms; De Rham complex; 35R01; 58J50; 47A55;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the multiplicity of the eigenvalues of the Hodge Laplacian on smooth, compact Riemannian manifolds of dimension five for generic families of metrics. We prove that generically the Hodge Laplacian, restricted to the subspace of co-exact two-forms, has nonzero eigenvalues of multiplicity two. The proof is based on the fact that the Hodge Laplacian restricted to the subspace of co-exact two-forms is minus the square of the Beltrami operator, a first-order operator. We prove that for generic metrics the spectrum of the Beltrami operator is simple. Because the Beltrami operator in this setting is a skew-adjoint operator, this implies the main result for the Hodge Laplacian.
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页码：3176 / 3193
页数：17
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