- #1

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I wonder if it is possible to write the

[itex]g^{\mu\nu} = \sum_{\mu}^{D}\sum_{\nu}^{D}

g_{_1}(x^{\mu})

g_{_2}(x^{\nu})[/itex]

where g

If no, then what would be a way of writing the components of a tensor? I dont like just g

*components*of the metric tensor (or any other tensor) as a summ of functions of the coordinates? Like this:[itex]g^{\mu\nu} = \sum_{\mu}^{D}\sum_{\nu}^{D}

g_{_1}(x^{\mu})

g_{_2}(x^{\nu})[/itex]

where g

_{1}and g_{2}are functions of one variable alone and D is the dimension of the Manifold. I hope you understand my poor English. Thanks in advance.If no, then what would be a way of writing the components of a tensor? I dont like just g

^{μ}^{ν}.... It would be better if there were a deeper way of representing that.
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