切丛和余切丛的全空间上的典范无挠的联络
Canonical Torsion-Free Connections on the Total Space of the Tangent and the Cotangent Bundle
摘要：
本文定义了基流形上的（余）切丛的全空间上的一类无挠无挠的联络，其中纤维的切空间与之平行.对于这些联络，纤维的每个切空间都是平坦的，并且从（余）切丛到基流形的正则投影是全测地的。在特殊情况下的连接是度量签名（n，n）或辛，并承认一个单一的平行全各向同性切n-平面。
英文摘要：
In this paper we define a class of torsion-free connections on the total space of the (co-)tangent bundle over a base-manifold with a connection and for which tangent spaces to the fibers are parallel. Each tangent space to a fiber is flat for these connections and the canonical projection from the (co-)tangent bundle to the base manifold is totally geodesic. In particular cases the connection is metric with signature (n,n) or symplectic and admits a single parallel totally isotropic tangent n-plane.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
