|Title of the article||
SOME LIFTS OF TENSOR FIELDS OF TYPE (1, R) WITH BASE IN ITS TANGENT BUNDLE
Sultanova Galiya Alievna, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), email@example.com
Background. Vector fields of type γG, GHγ,representing lifts of tensor field G∈ℑ11(M), defined on a smooth manifold M to the tangent bundle T(M), arise in the study of infinitesimal affine transformations with a complete lift. These lifts were introduced by K.Yano, Sh.Ishihara and used by F.I. Kagan in the study of infinitesimal affine, infinitesimal projective transformations equipped with full lift of torsion-free linear connection, defined on the basis of M, used by H.Shadyev when he described infinitesimal affine transformations of synectic lift of linear torsion-free connection with a smooth manifold M to its tangent bundle T(M). The purpose of this paper is to construct -γr lifts of tensor fields of type (1, r), (r ≥1) and explain some of their properties with respect to the differentiation of Lee and covariant differentiation.
smooth manifold, tangent bundle, lifts of tensor fields, tensor field, commutator of vector fields.
1. Yano K. and Ishihara S. Marcel Dek-ker, Inc. New York, 1973, pp. 12–25.
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