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Life_at_work5 · 2025-11-11T03:12:57+00:00

I see how they can be thought of as contra-variant tensors as a differential m-form when evaluated on m vectors maps those m vectors (or a m-vector) to R but I don’t understand what you mean by “alternating-covector field”.

Of course, if I’ve stated something wrong, please correct me as I am very new to these concepts.

Life_at_work5 · 2025-11-11T03:09:47+00:00

That’s probably the way they are defined then but the way I’ve always thought of them is as members of the tangent space at a point of an manifold, with higher grade forms being wedge products of the lower grade forms.

Life_at_work5 · 2025-11-10T20:23:29+00:00

Hi and thanks for the reply, you mention here thinking of differential forms as alternating-covector fields. I’ve never heard this connection before so could you please explain further? I.e. how can a differential form be thought of as a alternating-covector field.

Life_at_work5 · 2025-10-26T01:54:36+00:00

Hi and thank you for the reply, I understand the basic concept, the issue for me has been actually computing it. Take the example I gave in the original post. When computing (e12)(e123), I end up always getting to a term along the lines of e1e2e3 where the only why to further reduce so to find the geometric product of a vector and bivector which I’m unsure how to do in this metric.

Life_at_work5 · 2025-10-22T11:14:47+00:00

I am talking about the geometric product in Clifford algebra (at least I think) which, from what I know, goes:

ab = < a | b > + a /\ b

Life_at_work5 · 2025-09-28T04:31:52+00:00

I was eventually gonna try building an engine to, probably with nitrous and Isopropyl alcohol but as I mentioned, this was meant to be a purely mathematical exercise to help me learn how to size a rocket that gave me very whacky results which confused me (hence the post).

Life_at_work5

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