Re: Levi-Civita Symbol

On 31 May, 18:09, Igor <thoov...@xxxxxxxxxx> wrote:
On May 31, 1:04 pm, s...@xxxxxxxxxxxxx wrote:



On 31 May, 17:51, Igor <thoov...@xxxxxxxxxx> wrote:

On May 31, 9:56 am, "Christopher J. Henrich" <chenr...@xxxxxxxxxxxx>
wrote:

In article <wood-3105070643290...@xxxxxxxxxxxxxxxxxxxxxxxx>, J. B. Wood

<w...@xxxxxxxxxxxxxxxx> wrote:
Hello, all. My question: Is the subject symbol a tensor or not? Several
presumably authoritative references I have on tensor analysis seem to
disagree on this. Sincerely,

The thingamajig with three indices? Based on combining first
derivatives of the metric tensor? It definitely is not a tensor,
though it does arise in the theory of "tensor analysis."

One of the many good books on the subject is /Tensor/ /Analysis/, by
Synge and Schild. It's reprinted by Dover publications.

--
Chris Henrichhttp://www.mathinteract.com
The total lack of evidence is the surest sign that the conspiracy is working.

It sounds like you're confusing it with the Christoffel symbols,
otherwise known as affine connections.

Hmm... I was under the impression that the Levi-Civita symbol was just
the Christoffel symbol associated to the unique torsion-free metric-
compatible connection. Perhaps usage differs.

-Rotwang

I think part of the confusion is that, in some contexts, the
Christoffel is referred to as Levi-Civita. Check this out:

http://en.wikipedia.org/wiki/Levi-Civita_symbol

Oh, that thing? Right. But that isn't a tensor either. It's a tensor
*density* of weight one surely (meaning it picks up a factor of the
determinant of the Jacobian of a transformation)?

-Rotwang

.

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