Joint spectrum of the sub-Laplacian and the Reeb vector field on three-dimensional Heisenberg Bieberbach manifolds

2026/08/04 by Yoshiaki Suzuki, Yuya Takeuchi
Mathematics · #math.DG #math.AP #math.CV #msc:32V20 #msc:35R03 #msc:58C40

paper · pdf

27 pages

arxiv created 2026/08/04 · arxiv updated 2026/08/05

Abstract

A Heisenberg Bieberbach manifold is a compact quotient of the Heisenberg group by a discrete torsion-free subgroup of its pseudo-Hermitian automorphism group. In this paper, we study the joint spectrum of the sub-Laplacian and the Reeb vector field on three-dimensional Heisenberg Bieberbach manifolds. In particular, we explicitly compute the multiplicities of the joint spectrum using theta functions and the character theory of finite groups.

Citations

• The Folland-Stein spectrum of some Heisenberg Bieberbach manifolds
• Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds