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#### Kiwi

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1.) Am I correct to understand that the Einstein tensor notation used throughout the book is out of fashion and doesn't get used anymore? I don't see any of it on mathhelpboards.

Here is the Riemann Christoffel tensor in Einstein notation:

\(\nabla_i \nabla_j T^k - \nabla_j \nabla_j T^k = R^k_{mij}T^m \) where \(R^k_{mij}= \frac{\partial \Gamma^k_{jm}}{\partial Z^i}-\frac{\partial \Gamma^k_{im}}{\partial Z^j}+\Gamma^k_{in} \Gamma^n_{jm} - \Gamma^k_{jn} \Gamma^n_{im} \)

2.) Now it is obvious to me that this is valid in a space of any dimension. Is the same true for modern notation without any special thought or is it necessary in each dimension to come up with a new definition for the symbols in each space?

3.) As a simpler example in the tensor notation it is not necessary to define the cross product. What we know as the cross product in 3 dimensions can easily be expressed in Tensor notation and then extended to any dimension without much thought. Can the same be said of the modern notation?

4.) Is there a name for the modern notation?

Cheers

Dave