### Some articles on *tensor field, tensor fields, tensor, fields, field, tensors*:

Levi-Civita Symbol - Tensor Density - Ordinary Tensor

... In the presence of a metric

... In the presence of a metric

**tensor field**, one may define ordinary contravariant and contravariant**tensor fields**that agree with the Levi-Civita symbol ... These ordinary**tensor fields**should not be confused with each other, nor should they be confused with the**tensor**density**fields**mentioned above ... One of these ordinary**tensor fields**may be converted to the other by raising or lowering the indices with the metric as is usual, but a minus sign is needed if the metric signature contains an odd number of negatives ...Saint-Venant's Compatibility Condition - Rank 2

... of the vanishing of the Saint-Venant's

**Tensor Fields**... of the vanishing of the Saint-Venant's

**tensor**defined by The result that, on a simply connected domain W=0 implies that strain is the symmetric derivative of some vector**field**, was first ... non-simply connected domains there are finite dimensional spaces of symmetric**tensors**with vanishing Saint-Venant's**tensor**that are not the symmetric derivative of a vector**field**... and Poincare's lemma can be understood more clearly using the operator, where is a symmetric**tensor field**...Tensor (intrinsic Definition) -

... geometry, physics and engineering must often deal with

**Tensor Fields**... geometry, physics and engineering must often deal with

**tensor fields**on smooth manifolds ... The term**tensor**is in fact sometimes used as a shorthand for**tensor field**... A**tensor field**expresses the concept of a**tensor**that varies from point to point ...Mathematics Of General Relativity -

...

**Tensor Fields**in General Relativity...

**Tensor fields**on a manifold are maps which attach a**tensor**to each point of the manifold ... idea of a fibre bundle, which in the present context means to collect together all the**tensors**at all points of the manifold, thus 'bundling' them all into one grand object called the**tensor**bundle ... A**tensor field**is then defined as a map from the manifold to the**tensor**bundle, each point being associated with a**tensor**at ...### Famous quotes containing the word fields:

“It is not those who till the *fields* who eat fine rice, nor those who rear the silkworms who wear fine silks.”

—Chinese proverb.

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