Lens Spaces, Isospectral on Forms but not on Functions

Abstract

AbstractWe study the p-form spectrum of the Laplace-Beltrami operator acting on lens spaces as considered by Ikeda [Geometry of manifolds (Academic Press, Boston, MA, 1989) 383–417]. Ikeda gave examples of such spaces that are non-isometric but isospectral for all p ≤ p0. In this paper we exhibit examples of such spaces that are not isometric, and are isospectral for various, but not for all. values of p. In particular, examples are given of non-isometric lens spaces that are isospectral for some values of p but not for the case p = 0.