The gap of the eigenvalues for \(p\)-forms and harmonic \(p\)-forms of constant length
Denote by \(\lambda_k^{(p)}(M,g)\) the \(k\)-th positive eigenvalue of the Laplacian acting on \(p\)-forms on an oriented closed Riemannian manifold \((M,g).\) The following estimate is the main result of the paper: If all non-trivial harmonic \(p\)-forms have constant length and if the \(p\)-th Betti number satisfies \(b_p(M)\geq1\) then \(\lambda_k^{(p)}(M,g)\leq \lambda_0^{(p)}(M,g).\) In the last section examples are studied.
scientific article; zbMATH DE number 2182202