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Tensor Field

A tensor field of type (r,s) on a smooth manifold M assigns to each point p in M a tensor in

T_pM^( tensor r) tensor T_p^*M^( tensor s)

so that its components in every smooth coordinate chart are smooth functions. Equivalently, it is a smooth section of the corresponding tensor product bundle. A scalar field is a tensor field of type (0,0), a vector field has type (1,0), and a differential form is an alternating covariant tensor field.

See also

Differential k-Form, Tensor, Tensor Product, Vector Field

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References

Lee, J. M. Introduction to Smooth Manifolds, 2nd ed. New York: Springer-Verlag, 2013.

Cite this as:

Weisstein, Eric W. "Tensor Field." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TensorField.html

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