In the case 
case, there is a linear map, which is “linear approximation” of 
. In the manifold case, there is a similar linear map, but now it acts between tangent spaces. If 
and 
are smooth manifolds and 
is a smooth map then for each 
, the map
is defined by
is called the pushforward. Actually,
Suppose that 
and 
is a differentiable mapping. We have
Definition 1 The mapping 
is called a trivial fibration (differentiable) on if there exists a differential manifold 
, is called fibre of , and a diffeomorphism
such that the following diagram is commutative
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