Tensor density in sagemanifolds?

asked 2018-11-22 09:30:38 +0200

Dox gravatar image

Hello community.

I've just realized that within the class TensorField there are subclasses DiffForm and MultivectorField. I was wondering whether a maximal (i.e. rank $n$ in $n$ dimensions) differential form or multivector field are considered as tensor densities. I'm thinking in the Levi-Civita epsilon.

Well, more generally... Is there a way to assign a density weight to a tensor?

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I don't think this is implemented yet. To implement tensor densities I guess TensorField should become a subclass of TensorDensity (or TensorDensityField?) with weight zero, and probably much functionality could be moved to TensorDensity with the appropriate generalization (taking the weight into account).

rburing gravatar imagerburing ( 2018-11-22 10:11:38 +0200 )edit

Yes I confirm that tensor densities are not implemented yet. In particular, the method PseudoRiemannianMetric.volume_form() returns a tensor field (a $n$-form), not a tensor density.

eric_g gravatar imageeric_g ( 2018-11-22 14:16:29 +0200 )edit

Btw, if you would like to implement tensor densities, please visit https://sagemanifolds.obspm.fr/contri....

eric_g gravatar imageeric_g ( 2018-11-22 15:31:44 +0200 )edit