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from Part I - Elements of differential geometry
Published online by Cambridge University Press: 30 May 2024
Tensors and tensor densities of arbitrary rank on arbitrary differentiable manifolds are defined and described. The difference between covariant and contravariant vectors is explained and illustrated with examples. Mappings between manifolds and the associated mappings of tensors are discussed, and it is shown that coordinate transformations are examples of such mappings. The Levi-Civita symbols and multidimensional Kronecker deltas are defined, and their usefulness in calculations involving determinants is demonstrated.
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