Fibered manifold

In differential geometry, in the category of differentiable manifolds, a fibered manifold is a surjective submersion $${\displaystyle \pi :E\to B\,}$$ that is, a surjective differentiable mapping such that at each point ${\displaystyle y\in E}$ the tangent mapping $${\displaystyle T_{y}\pi :T_{y}E\to T_{\pi (y)}B}$$ is surjective, or, equivalently, its rank equals ${\displaystyle \dim B.}$