论文标题
沿平行张量沿空间形式的平行张量和由顶点代数结构激发的猜想的协变量的衍生物
Covariant derivatives of eigenfunctions along parallel tensors over space forms and a conjecture motivated by the vertex algebraic structure
论文作者
论文摘要
我们在完整的，连接的Riemannian歧管上研究了Laplace-Beltrami操作员特征功能的协变量，该衍生物具有非零恒定截面曲率。我们表明，沿每个平行张量，协变量导数是本征函数的标量倍数。我们还表明，标量取决于特征值并证明某些特性。还宣布了由顶点代数结构的研究所激发的猜想，这表明在这些多项式中存在有趣的结构，这些结构正在等待进一步的探索。
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.
