Covariant derivatives of eigenfunctions along parallel tensors over space forms and a conjecture motivated by the vertex algebraic structure

Journal of noncommutative geometry

article

Fei Qi¹ 

[1] University of Manitoba

关键词: Covariant derivatives;    parallel tensors;    eigenfunctions;    space forms;    theory of invariants;   

DOI  :  10.4171/jncg/472

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

We study the covariant derivatives of an eigenfunction for the Laplace–Beltrami operator on a complete, connected Riemannian manifold with nonzero constant sectional curvature. We show that along every parallel tensor, the covariant derivative is a scalar multiple of the eigenfunction. We also show that the scalar is a polynomial depending on the eigenvalue and prove some properties. A conjecture motivated by the study of vertex algebraic structure on space forms is also announced, suggesting the existence of interesting structures in these polynomials that awaits further exploration.

【 授权许可】

CC BY