Hi, everyone:(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to produce a V.Field that is 0 only at one point of S^2.

I have been thinking of using the homeo. between S^2-{pt.} and

R^2 to do this. Please tell me if this works:

We take a V.Field on R^2 that is nowhere zero, but goes to 0

as (x,y) grows (in the sense that it "goes to oo" in the Riemann sphere), and

then pulling it back via the stereo projection.

We could use, e.g:

V(x,y)=( 1/(X^2+1), 1/(Y^2+1))

For the pullback. Does this work?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Vector Fields on S^2, 0 only at 1 point.

**Physics Forums | Science Articles, Homework Help, Discussion**