Horizontal lifts from a manifold to its cotangent bundle
Horizontal lifts from a manifold to its cotangent bundle
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从流形到其余切丛的水平升力
DOI：
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发表时间：
1967
期刊：
影响因子：
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通讯作者：
E. Patterson
中科院分区：
文献类型：
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作者：
K. Yano;E. Patterson
最近的一篇文章[4]中引入了类$C^{infty}$的$M$到它的余切丛$cT（M）$的概念。定义了$（1，1）$或$（1，2）$类型的函数、向量场、l-形式和张量场的垂直提升。完全提升的定义仅限于向量场、$（1，1）$型张量场和$（1，2）$型反对称张量场。在每一种情况下，张量场的完全提升都具有与原始张量场相同的类型;然而垂直提升不具有这种性质。在本文的S2中，我们总结了相关公式的细节。在本文中，我们介绍了另一种类型的“电梯“从$M$到
$M$ of class $C^{infty}$ to its cotangent bundle $cT(M)$ were introduced in a recent paper, [4]. Vertical lifts of functions, vector fields, l-forms and tensor fields of type $(1, 1)$ or $(1, 2)$ were defined. The definitions of complete lifts were restricted to vector fields, tensor fields of type $(1, 1)$ and skew-symmetric tensor fields of type $(1, 2)$ . In each case, the complete lift of a tensor field has the same type as the original; however vertical lifts do not have this property. In S 2 of the present paper, we summarise the details of the relevant formulae. In the present paper we introduce another type of ” lift ” from $M$ to