AI 中文总结
本文研究三维Heisenberg Bieberbach流形上次拉普拉斯算子与Reeb向量场的联合谱，利用theta函数和有限群特征理论明确计算了其重数。
AI 中文摘要
Heisenberg Bieberbach流形是Heisenberg群在其伪Hermitian自同构群的无挠离散子群作用下的紧商空间。本文研究三维Heisenberg Bieberbach流形上次拉普拉斯算子与Reeb向量场的联合谱，特别利用theta函数和有限群的特征理论明确计算了该联合谱的重数。
英文摘要
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.
Comments27 pages
