LIFTINGS OF TENSOR FIELDS TO THE COTANGENT BUNDLE

Miroslav Doupovec and Jan Kurek

Key words: Natural operator, tensor field, cotangent bundle.

1991 Math. Subject Classification: 53A55, 58A20.

We study geometrical constructions transforming tensor fields of type
$(r,s)$ to the cotangent bundle. We present the full classification of
all such natural operators in the cases $(r,s)=(0,1)$,
$(r,s)=(0,2)$ and $(r,s)=(1,1)$. We also study some
geometrical constructions of $(p,q)$--tensor fields on $T^*M$ by means
of $(r,s)$--tensor fields on $M$, $(r,s)\ne(p,q)$.