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Lift; tensor bundle; pure tensor; operator Yano--Ako
In this paper we consider a method by which a skew-symmetric tensor field of type (1,2) in $M_{n}$ can be extended to the tensor bundle $T_q^0(M_n)$ $(q>0)$ on the \textit{pure cross-section.} The results obtained are to some extend similar to results previously established for cotangent bundles $T_{1}^{0}(M_{n})$. However, there are various important differences and it appears that the problem of lifting tensor fields of type (1,2) to the tensor bundle $T_{q}^{0}(M_{n})$ $(q>1)$ on the \textit{pure cross-section} presents difficulties which are not encountered in the case of the cotangent bundle.
[1] Ledger A., Yano K.: Almost complex structures on tensor bundles. J. Dif. Geom. 1 (1967), 355–368. MR 0226560 | Zbl 0157.28402
[2] Salimov A. A., Magden A.: Complete lifts of tensor fields on a pure cross-section in the tensor bundle $T_{q}^{1}(M_{n})$. Note di Matematica 18, 1 (1998), 27–37. MR 1759013
[3] Cengiz N., Salimov A. A.: Complete lifts of derivations to tensor bundles. Bol. Soc. Mat. Mexicana (3) 8, 1 (2002), 75–82. MR 1916892 | Zbl 1020.53006
[4] Yano K., Ako M.: On certain operators associated with tensor fields. Kodai Math. Sem. Rep. 20 (1968), 414–436. MR 0234370 | Zbl 0167.19702
[5] Salimov A. A.: Generalized Yano–Ako operator and the complete lift of tensor fields. Tensor N. S., Tensor Soc. of Japan 55, 2 (1994), 142–146. MR 1310107 | Zbl 0818.53032
[6] Cengiz N., Salimov A. A.: Diagonal lift in the tensor bundle and its applications. Appl. Math. Comput. 142, 2–3 (2003), 309–319. MR 1979438 | Zbl 1034.53016
[7] Salimov A. A., Cengiz N.: Lift of Riemannian metrics to tensor bundles. Russian Math. (IZ. VUZ) 47, 11 (2003), 47–55. MR 2038854
[8] Magden A., Cengiz N., Salimov A. A.: Horizontal lift of affinor structures and its applications. Appl. Math. Comput. 156, 2 (2004), 455–461. MR 2087522 | Zbl 1073.53044
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