Examples
- A classical covariant derivative or affine connection defines a connection on the tangent bundle of M, or more generally on any tensor bundle formed by taking tensor products of the tangent bundle with itself and its dual.
- The Levi-Civita connection is a connection on the tangent bundle of a Riemannian manifold.
- The exterior derivative is a flat connection on E = M × R (the trivial line bundle over M).
- More generally, there is a canonical flat connection on any flat vector bundle (i.e. a vector bundle whose transition functions are all constant) which is given by the exterior derivative in any trivialization.
Read more about this topic: Connection (vector Bundle)
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