Geodesic
On applications of the Yano–Ako operator
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 45 (2006) no. 1, pp. 135-141 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 53A45, 53C05, 53C15, 53C25, 53C55
Keywords: Lift; tensor bundle; pure tensor; operator Yano--Ako 
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Magden, A.; Salimov, A. A. On applications of the Yano–Ako operator. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 45 (2006) no. 1, pp. 135-141. http://geodesic.mathdoc.fr/item/AUPO_2006_45_1_a12/