Transform Calc on S^3 to S^2: Maifold Calculus

[htaati]

how can I transform my calculation on S^3 to the S^2.
for example a trace or a Fourier transform

 

[mathwonk]

hopf map? consider R^4 as C^2, the complex 2 space, and consider all complex "lines" in C^2. this family of complex subspaces is homeomorphic to S^2, hence this fibres S^3 over S^2 with fibers equal to circles. this is the famous hopf map from S^3 to S^2.

 

[htaati]

manifold calculus

hopf map? consider R^4 as C^2, the complex 2 space, and consider all complex "lines" in C^2. this family of complex subspaces is homeomorphic to S^2, hence this fibres S^3 over S^2 with fibers equal to circles. this is the famous hopf map from S^3 to S^2.

well my problem is: I have an integral in S^3 . I want to calculate this integral.
i) in S^3.
ii) how can I transform this integral to S^2.

If you think that you need more explanation I would be glad to
sent it for you.

 

[mathwonk]

you might try to generalize the fubini theorem, i.e. integrate over the fibering circles first and then integrate those integrals over the 2 sphere.

but this is only indicated if the quantity being integrated somehow restects the compex circles in the hopf fibration.

 

[Norb]

May be Maple atlas package can help to make some real calculations.
See http://www.mathshop.digi-area.com/prod/atlas/index.php
It can make calculations for manifolds and mapping one into another.