黎曼局部对称空间的 Calabi 算子
微分几何
2024-10-24 v5
摘要
在常曲率黎曼流形上，Calabi 算子是一个二阶线性微分算子，为 Killing 算子的值域提供局部可积条件。我们将该算子推广，以在可能时为黎曼局部对称空间提供二阶线性局部可积条件。具体而言，我们证明了该广义算子在不可约情形下总是有效，并精确指出了那些使其失效的乘积情形。
引用
@article{arxiv.2112.00841,
title = {A Calabi operator for Riemannian locally symmetric spaces},
author = {Federico Costanza and Michael Eastwood and Thomas Leistner and Benjamin McMillan},
journal= {arXiv preprint arXiv:2112.00841},
year = {2024}
}
备注
17 pages. A spelling mistake has been corrected. Our proof of Proposition 5 has been improved. A missing curvature term has been added to (31): it does not effect the subsequent argument. Several improvements have been made. We now avoid using the Ambrose-Singer holonomy theorem