- #1
mikeph
- 1,235
- 18
Hello,
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
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