Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Intersection of complex sphere and cone

  1. Oct 18, 2010 #1
    Show the intersection of complex sphere (|z1|^2+|z2|^2+|z3|^2=1) in C^3 and the complex cone (z1^2+z2^2+z3^3=1) in C^3 is a smooth submanifold of C^3.

    I am trying to do it using regular level set, but I am not sure which one of (1,0) or (1,1,0) should be set to be the regular value?
  2. jcsd
  3. Oct 20, 2010 #2
    You have a map from C^3 to R x C. The intersection is the preimage of (1,1,0).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook