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

Surface integrals in R^n, n>3

  1. Nov 9, 2009 #1
    How would I calcluate a surface integral in dimensions greater than 3.

    For example, from the definition of a surfrace integral over a vector field: http://en.wikipedia.org/wiki/Surface_integral#Surface_integrals_of_vector_fields

    To compute the surface integral, I would first need a vector normal to the vector field. In R^3 this is just done by using the cross product. Is there a general way to find a normal vector when not in R^3, since the cross product is no longer valid?
     
  2. jcsd
  3. Nov 9, 2009 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Actually, what you need is the a bivector tangent to the surface.

    That trick works in R3 because bivectors can be identified with "axial vectors". However, in R4, the dual would be some sort of "axial bivector", and in R5 it would be an "axial trivector" -- so we can't use this trick anymore.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Surface integrals in R^n, n>3
  1. Special region of R}^n (Replies: 0)

  2. Compact subset of R^n (Replies: 2)

  3. Open Sets of R^n (Replies: 4)

Loading...