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MiS Preprint
12/2000
Note on the spectrum of the Hodge-Laplacian for k-forms on minimal Legendre submanifolds in S^(2n+1)
Knut Smoczyk
Abstract
Given a minimal Legendre immersion L in S2n+1 and n >= k >= 1 we prove that n+1-k is an eigenvalue of the Hodge-Laplacian acting on k and (k-1)-forms on L. In particular we show that the eigenspaces Eigk(n+1-k) and Eigk-1(n+1-k) are at least of dimension $\frac{n}{k}$. The paper was motivated by an earlier result of the author concerning minimal Lagrangian immersions in hyperKähler manifolds.
