By "intrinsic", I mean, something which doesn't depend choice of coordinates.
I think this is true, but is this actually a theorem that is written in some book?
Is there some sort of "classification theorem" of this type in higher dimensions?
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Note that if we know it comes from the curvature, then, we have decomposition theorems as in https://math.stackexchange.com/questions/295309/are-the-ricci-and-scalar-curvatures-the-only-interesting-tensors-coming-from-t But, why does it have to come from curvature...? – Hausdorff Sep 24 '20 at 20:08
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This paper might be of some interest. – Kajelad Sep 24 '20 at 21:15