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Sep 10, 2020 at 14:47 comment added Willie Wong How exactly are you defining torsion then? On a real differential manifold with an affine connection, the torsion tensor is manifestly real by definition. You can't just slot in complex values and hope it would work out.
Sep 10, 2020 at 14:37 comment added Eris @WillieWong sure, I edited the question. I'm not specifically on a complex manifold but I'm trying to understand what kind of manifold would result from such a choice of a complex torsion.
Sep 10, 2020 at 14:35 comment added Eris Thanks YCor. Both Axial-vector and Axial are used in literature.
Sep 10, 2020 at 14:34 history edited Eris CC BY-SA 4.0
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Sep 10, 2020 at 14:32 comment added Willie Wong 24 components only in certain spatial dimensions, you should probably specify the dimension (I think you mean 4 dimensions, since the "axial vector part" is determined by a three form.) Also; please explain what you mean by "complex". Are you working with an almost complex manifold?
Sep 10, 2020 at 14:11 comment added YCor (I fixed "axialvector part" to "axial vector part" but maybe it should be "axial part", please check.)
Sep 10, 2020 at 14:10 comment added YCor Related: What is torsion in differential geometry intuitively?
Sep 10, 2020 at 14:08 history edited YCor CC BY-SA 4.0
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Sep 10, 2020 at 14:06 review First posts
Sep 10, 2020 at 14:06
Sep 10, 2020 at 14:02 history asked Eris CC BY-SA 4.0