193:) representation are a more suitable topic for an encyclopedia article (tensors of type ρ). Unfortunately, there seems to be little agreement as to where one draws the line. For instance, must all tensor bundles be associated bundles of the tangent bundle? Or is one allowing a more general principal bundle besides the frame bundle? The former requirement is clearly the case in most uses of the term "tensor" in physics and analysis, where the tensor intertwines the action of diffeomorphisms with a linear transformation of the fibre. To make matters worse, determinantal representations of GL(
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I see. I don't see any reason to not mention this panoply of definitions, but one thing to keep in mind is the fact that various articles link to this page, and they don't all refer to the current definition in here, e.g.
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Shouldn't the tensor bundle be defined as the tensor products of the tangent bundle and the cotangent bundles instead of the direct sum of those?
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While it is certainly true that doing calculus for arbitrary tensor fields requires a
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of an antisymmetric differentiable tensor field is well defined even without one.
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tensor bundle", which is common parlance for the bundle whose fibre is the full
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Upon searching google books, I found various definitions. Many of them defined
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wants the tensor bundle to be the tensor algebra of any vector bundle, and
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