The Principle of Relativity

by Albert Einstein; H. Minkowski

In the symmetrical case treated, (41) can be replaced by either of the forms

"(41a)"

or

"(41b)"

which we shall have to make use of afterwards.

§12. The Riemann-Christoffel Tensor.

We now seek only those tensors, which can be obtained from the fundamental tensor g^μν by differentiation alone. It is found easily. We put in (27) instead of any tensor A^μν the fundamental tensor g^μν and get from it a new tensor, namely the extension of the fundamental tensor. We can easily convince ourselves that this vanishes identically. We prove it in the following way; we substitute in (27)