Geodesic
Natural liftings of $(0,2)$-tensor fields to the tangent bundle
Archivum mathematicum, Tome 30 (1994) no. 3, pp. 215-225.

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We determine all first order natural operators transforming $(0,2)$–tensor fields on a manifold $M$ into $(0,2)$–tensor fields on $TM$.
Classification : 53A55, 53C15, 58A20
Keywords: natural operator; tensor field; complete lift; vertical lift 
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     author = {Doupovec, Miroslav},
     title = {Natural liftings of $(0,2)$-tensor fields to the tangent bundle},
     journal = {Archivum mathematicum},
     pages = {215--225},
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     volume = {30},
     number = {3},
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     zbl = {0816.53007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1994__30_3_a4/}
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Doupovec, Miroslav. Natural liftings of $(0,2)$-tensor fields to the tangent bundle. Archivum mathematicum, Tome 30 (1994) no. 3, pp. 215-225. http://geodesic.mathdoc.fr/item/ARM_1994__30_3_a4/