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Josef Janyška (2005)
Open Mathematics
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We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the 2nd order valued reduction theorems we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection.
Ivan Kolár (1996)
Extracta Mathematicae
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We present a survey of some recent results about natural operations on the r-th order tangent bundle and similar objects.
Miroslav Doupovec, Ivan Kolář (1991)
Archivum Mathematicum
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Jacek Dębecki (2006)
Annales Polonici Mathematici
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We give a classification of canonical tensor fields of type (p,0) on an arbitrary Weil bundle over n-dimensional manifolds under the condition that n ≥ p. Roughly speaking, the result we obtain says that each such canonical tensor field is a sum of tensor products of canonical vector fields on the Weil bundle.
Kolář, Ivan
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Jacek Dębecki (2007)
Annales Polonici Mathematici
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This paper contains a classification of all linear liftings of symmetric tensor fields of type (1,2) on n-dimensional manifolds to any tensor fields of type (1,2) on Weil bundles under the condition that n ≥ 3.