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Natural tensor fields of type \((0,2)\) on the tangent and cotangent bundles of a Fedosov manifold. (English) Zbl 1109.53031
Summary: To any \((0,2)\)-tensor field on the tangent and cotangent bundles of a Fedosov manifold, we associate a global matrix function ‘mutatis mutandis’ as in the semi-Riemannian case. Based on this fact, natural \((0,2)\)-tensor fields on these bundles are defined and characterized.
MSC:
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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