Suppose I have a triangle defined by 3 unit vectors {$v_1, v_2, v_3$} in a 3 dimensional complex inner product space.
What would be the centre of such a triangle? I guess it should be something like $(v_1+v_2+v_3)/3$.
How about if the 3 vectors define a spherical triangle on the unit sphere? Is it just a case of taking the vector in the paragraph above and projecting it onto the unit sphere? Are there any other possible candidates which I imagine may make use of the inner products of the 3 vectors?
Thanks for your help,
Stan
EDIT ----
So to perhaps make my question clearer, how would I go about finding the incenter of a spherical triangle?