Maifold calculus

1. Nov 4, 2005

htaati

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

2. Nov 6, 2005

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.

3. Nov 6, 2005

htaati

manifold calculus

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.

4. Nov 6, 2005

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.

5. Nov 10, 2005

Norb

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

Last edited by a moderator: May 2, 2017