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Say you have a function f on the domain R^n, and an integral transform P which integrates f over all possible straight lines in R^n. I am lead to believe that the range of this is R^(2n), or a tangent bundle, which I am having MASSIVE problems visualising!

Am I right in saying the tangent bundle can be described by the multiplication of a vector on the unit sphere in R^n with a vector in R^n, ie. all points, then from each point, subtending all angles?

But surely this creates duplication? ie. for n=3, the line passing point (0,0,0) parallel to (1,0,0) must be the same as the line passing through (1,0,0) parallel to (1,0,0). So I am trying to picture a more "efficient" way to specify the range of this transform...

Is it completely described by all vectors in R^n perpendicular to each plane described by the vector on the unit sphere in R^n? How many are there per plane?

SO confused! But intrigued....

Thanks,

Mike

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# Trying to get my head around tangent bundles

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