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pmb_phy is offline
Aug11-04, 05:35 PM
P: 2,955
Quote Quote by mathwonk
In that same spirit, on the site

the symbols dx^j in equation (1) should be bold, since they are the entirely analogous basic covariant 1-tensors.
The components of tensors are in italics.
The fact that they are not bold, leads to the confusion that this expression denotes a 0 - tensor instead of a 2 - tensor,
That expression is a tensor of rank 0. If you notice, it is the contraction of a second rank covariant tensor with two rank 1 tensors. Such a contraction is always a tensor of rank zero. Why do you keep calling the interval a dstensor?
i.e. equation (1) is a sum of, scalar multiples of, pairwise products of, basic 1 tensors,

hence it is a homogeneous "polynomial" of degree 2 in the basic 1 tensors,

i.e. a 2-tensor.

Does that seem believable?
Nope. Sorry.