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.


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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