Tensor
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1 Definition
Let be a smooth manifold and vector bundles over . A tensor (field) is a section in the bundle of bundle homomorphisms between and . Alternatively, a tensor can be viewed as a -linear map which means
(1)
Tex syntax errorf \in C^\infty(M)s\in \Gamma E$.
The bundle may be itself a tensor product of vector bundles . Then a tensor may be
viewed as a -multilinear map .