The Flat Case
When M is a Euclidean space and all the fields are taken to be invariant by translations by the vectors of M, we get back to a situation where a tensor field is synonymous with a tensor 'sitting at the origin'. This does no great harm, and is often used in applications. As applied to tensor densities, it does make a difference. The bundle of densities cannot seriously be defined 'at a point'; and therefore a limitation of the contemporary mathematical treatment of tensors is that tensor densities are defined in a roundabout fashion.
Read more about this topic: Tensor Field
Famous quotes containing the words flat and/or case:
“Man is a wingless animal with two feet and flat nails.”
—Plato (c. 427347 B.C.)
“We all know the Navy is never wrong, but in this case it was a little weak on being right.”
—Wendell Mayes, U.S. screenwriter. Otto Preminger. CINCPAC II (Henry Fonda)