Note on the spectrum of the Hodge-Laplacian for k-forms on minimal Legendre submanifolds in S^(2n+1)

Knut Smoczyk

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Submission date: 29. Feb. 2000
Pages: 8
published in: Calculus of variations and partial differential equations, 14 (2002) 1, p. 107-113 
DOI number (of the published article): 10.1007/s005260100095
Bibtex

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 Eig_k(n+1-k) and Eig_k-1(n+1-k) are at least of dimension . The paper was motivated by an earlier result of the author concerning minimal Lagrangian immersions in hyperKähler manifolds.