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The Cotton tensor in Riemannian spacetimes. (English) Zbl 1045.83051
The Cotton tensor is systematically investigated in an arbitrary dimension $$n$$ of the spacetime. Its relation to the Bach tensor, to properties of conformal invariance, to Bianchi identities, and to the Einstein field equation is presented. Especially, the numbers of independent components in dependence on $$n$$ of each of these items is given. Several examples elucidate the presented results.

##### MSC:
 83C80 Analogues of general relativity in lower dimensions 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory 53Z05 Applications of differential geometry to physics
##### Keywords:
Bianchi identity; Bach tensor; Einstein equation
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