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On applications of the Yano-Ako operator. (English) Zbl 1129.53015

The authors consider a method by which a skew-symmetric tensor field of type \((1,2)\) in \(M_n\) can be extended to the tensor bundle \(T^0_{q}(M_n)\) \((q>0)\) on the pure cross-section. The results obtained are to some extend similar to results previously established for cotangent bundles \(T^0_{1}(M_n)\). However, there are various important differences and it appears that the problem of lifting tensor fields of type \((1,2)\) to the tensor bundle \(T^0_{q}(M_n)\) \((q>1)\) on the pure cross-section presents difficulties which are not encountered in the case of the cotangent bundle.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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References:

[1] Ledger A., Yano K.: Almost complex structures on tensor bundles. J. Dif. Geom. 1 (1967), 355-368. · 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. · Zbl 0976.53014
[3] Cengiz N., Salimov A. A.: Complete lifts of derivations to tensor bundles. Bol. Soc. Mat. Mexicana (3) 8, 1 (2002), 75-82. · Zbl 1020.53006
[4] Yano K., Ako M.: On certain operators associated with tensor fields. Kodai Math. Sem. Rep. 20 (1968), 414-436. · Zbl 0167.19702 · doi:10.2996/kmj/1138845745
[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. · 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. · Zbl 1034.53016 · doi:10.1016/S0096-3003(02)00305-3
[7] Salimov A. A., Cengiz N.: Lift of Riemannian metrics to tensor bundles. Russian Math. (IZ. VUZ) 47, 11 (2003), 47-55. · Zbl 1078.53511
[8] Magden A., Cengiz N., Salimov A. A.: Horizontal lift of affinor structures and its applications. Appl. Math. Comput. 156, 2 (2004), 455-461. · Zbl 1073.53044 · doi:10.1016/j.amc.2003.08.004
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