Re: Multidimensional manifolds

Alen wrote:
On Sep 26, 7:31 am, Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
The "^" introduces superscripts, and the "_" introduces subscripts [...]

I know, but that way of writing is often hard to read. I just think
using capitals and small letters can be easier.

But you omit which are sub- and which are super-scripts. That's important. I found your equation rather obscure. Conventions are important, as they assist communication; making up new ones is counter-productive unless they are a clear and obvious improvement. Yours is clearly worse than the usual nomenclature around here.


I studied Levi-Civita, which I thought was good, until he gets
to the Christoffel symbols and the horrendous Riemann
tensor. I am convinced there is a better way than that to
specify the geometry of a curved manifold.

Hmmm. Cartan introduced curvature 2-forms. I'm not sure they are any simpler. Indeed, there is no simple way to specify the geometry. Given a geometry (i.e. its metric), the Riemann tensor is unique, so no simpler way is possible (Cartan's 2-forms are equivalent).

Except, of course, for simpler situations. For instance in
2 dimensions things simplify a lot.


Tom Roberts
.

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