It is known that a tensor field is a tensor-valued function T=T(p) whose argument p is a point of some space (or some manifold). However, in physics some tensor fields are produced from other tensor fields, e. g. Lagrangians in physical field theories including tensorial fields:(adsbygoogle = window.adsbygoogle || []).push({});

L=L(p,T(p),\nabla T(p)).

Exact mathematical treatement of such tensor fields with additional tensorial arguments is given in my paper

http://arxiv.org/abs/math/0503332

I invite to discuss this paper and its possible applications. One can also use this paper in order to test his/her understanding of tensors at all.

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# An extension of the concept of a tensor field

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