- #1

kent davidge

- 933

- 56

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 don't 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 don't like just g

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