Abstract
The horizontal and complete lifts from a manifold Mn to its cotangent bundles were studied by Yano and Ishihara, Yano and Patterson, Nivas and Gupta, Dambrowski, and many others. The purpose of this paper is to use certain methods by which fλ(7, 1)‐structure in Mn can be extended to . In particular, we have studied horizontal and complete lifts of fλ(7, 1)‐structure from a manifold to its cotangent bundle.
Highlights
Let M be a differentiable manifold of class c∞ and of dimension n and let CTM denote the cotangent bundle of M
In order that the complete lift of f C of a (1,1) tensor field f admitting fλ(7, 1)-structure in M may have the similar structure in the cotangent bundle CTM, it is necessary and sufficient that
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Summary
Let M be a differentiable manifold of class c∞ and of dimension n and let CTM denote the cotangent bundle of M. The following are notations and conventions that will be used in this paper The Lie product of vector fields X and Y is denoted by [X,Y ]. Any point p ∈ Π−1(A) is denoted by the ordered pair (A, pA), where p is 1-form in M and pA is the value of p at A. U induces a coordinate neighborhood Π−1(U) in CTM and p ∈ Π−1(U). Let fih be components of f at A in the coordinate neighborhood U of M. The complete lift f c of f is a tensor field of type (1,1) in CTM whose components fBA in Π−1(U) are given by [2].
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