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Vector/Algebra valued differential forms

asked 2021-08-12 20:32:20 +0200

VonbatenBach gravatar image

Hi, I'm new to Sage and curious about one, potentially very useful aspect regarding SageManifolds module. I've seen that part regarding vector bundles is already developed, so I'd like to ask whether it is possible to form objects such as differential forms on regular manifold M, valued in vector bundle E.

More precisely, structures such as C^{\infty} ( E \otimes \bigwedge^k (T^{\ast} M ) ) (sorry, I can't insert pictures yet). Such entities arise naturally, at least in physics (starting from general relativity) where one needs to relate structure of vector bundle over M with tangent bundle of M.

In index notation, which also works in Sage, such tensors would be naturally manipulated by structure on M and E. Is there a possibility to form such differential forms, any other way than just forming a matrix of regular differential forms? Making such a matrix would be an option in the most trivial cases, but in general one would rather like to treat E and M equally.

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answered 2021-08-14 12:29:45 +0200

mjungmath gravatar image

updated 2021-08-14 12:32:58 +0200

Thank you for your interest. Unfortunately, vector-valued differential forms are not supported yet.

Nevertheless, I had already opened a ticket on this (#28640) with a rough idea how it could work out, but then I got busy with other things and priorities have shifted.

Indeed, the project would very much benefit from this feature. If you are interested to contribute, here is a short tutorial how this works. If you have any further questions, please don't hesitate to ask Eric or me, we would be very happy to help you.

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Asked: 2021-08-12 20:32:20 +0200

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Last updated: Aug 14 '21