Riemannian metrics with large first eigenvalue on forms of degree \(p\). (English) Zbl 0848.53022

Gentile, G.; Pagliara, V.

Proc. Am. Math. Soc. 123, No. 12, 3855-3858 (1995).

Let \((M,g)\) be a compact, connected \(C^\infty\) Riemannian manifold of \(n\) dimensions and \(\lambda_{1,p} (M,g)\) the first nonzero eigenvalue of the Laplace operator acting on differential forms of degree \(p\). The authors prove that for \(n \geq 4\) and \(2 \leq p \leq n - 2\), there exists a family of metrics \(g_t\) of volume one, such that \(\lambda_{1,p}(M,g_t) \to \infty\) as \(t \to \infty\).

Reviewer: M.Puta (Timişoara)

MSC:

53C20	Global Riemannian geometry, including pinching
58J50	Spectral problems; spectral geometry; scattering theory on manifolds

Keywords:

Laplacian on \(p\)-forms; first eigenvalue; family of metrics