Gaps in the differential forms spectrum on cyclic coverings |
| |
Authors: | Colette Anné Gilles Carron Olaf Post |
| |
Affiliation: | 1.Faculté des Sciences, Laboratoire de Mathématiques Jean Leray,Université de Nantes, CNRS,Nantes,France;2.Institut für Mathematik,Humboldt-Universit?t zu Berlin,Berlin,Germany |
| |
Abstract: | We are interested in the spectrum of the Hodge–de Rham operator on a -covering X over a compact manifold M of dimension n + 1. Let Σ be a hypersurface in M which does not disconnect M and such that M − Σ is a fundamental domain of the covering. If the cohomology group H n/2(Σ) is trivial, we can construct for each a metric g = g N on M, such that the Hodge–de Rham operator on the covering (X, g) has at least N gaps in its (essential) spectrum. If , the same statement holds true for the Hodge–de Rham operators on p-forms provided . |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|