Tensor field

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A tensor field (also imprecise tensor) is examined in the mathematical sub-area of differential geometry, in particular in tensor analysis. It is a function that assigns a tensor to each point of an underlying space in a special way .


Let be a smooth manifold and an (r, s) - tensor bundle . An (r, s) -tensor field is a smooth cut in the tensor bundle . The number of tensor fields is denoted by. This set is a module on the algebra of smooth functions .


Let M be a differentiable manifold, then a tensor field on M is a mapping that assigns a tensor to every point.

See also


  • R. Abraham, JE Marsden, T. Ratiu: Manifolds, Tensor Analysis, and Applications (= Applied Mathematical Sciences 75). 2nd edition. Springer-Verlag, New York NY et al. 1988, ISBN 0-387-96790-7 .

Web links

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