Vertical and complete lifts from a manifold to its cotangent bundle
Vertical and complete lifts from a manifold to its cotangent bundle
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从流形到其余切丛的垂直完整提升
DOI：
10.2969/jmsj/01910091
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发表时间：
1967
影响因子：
0.7
通讯作者：
E. Patterson
中科院分区：
文献类型：
--
作者：
K. Yano;E. Patterson
本章讨论了M中某些类型的张量场可以推广到c T（M）的各种方法，以给出关于两个流形结构之间关系的有用信息。本章重点介绍向量场、张量场（1，1）型和反对称张量场（1，2）型的完全提升。在每一种情况下，完全升力都被定义为与原始升力相同类型的张量场。一般来说，张量场的垂直提升与原始张量场的垂直提升的类型不同;然而这种构造是有用的。这些方法能够检验CT（M）的结构与M的结构的关系。特别是，它示出了如何几乎复杂和相似的结构M可以扩展到CT（M）。升降机仿射连接在M也检查，使用的想法的黎曼扩展。
Publisher Summary This chapter considers various methods by which certain types of tensor fields in M can be extended to c T (M) to give useful information about the relationships between the structures of the two manifolds. The chapter focuses on complete lifts of vector fields, tensor fields of type (1, 1) and skewsymmetric tensor fields of type (1, 2). In each of these cases, the complete lift is defined to be a tensor field of the same type as the original. In general, the vertical lift of a tensor field does not have the same type as the original; nevertheless the construction is a useful one. The methods enable to examine the structure of C T( M ) in relation to that of M. In particular, it is shown how almost complex and similar structures on M can be extended to C T(M). Lifts of affine connections in M is also examined, using the idea of a Riemann extension.