The problem of lifting tensor fields on the cross-section of tensor bundles, which is also called an n-dimensional submanifold, has been considered by several authors, including K. Yano, C. S. Houh, and S. Ishihara, and A. A. Salimov and A. Magden. K. Yano [1,2] (for details, also see [3]) studied the behavior on the cross-section of the lifts of an almost complex structure on a manifold M to its tangent bundle T(M) and its cotangent bundle T~*(M).
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