- #1
- 3,330
- 715
Given is the second order equation,
##X_{uv} = A(u,v)X_{u} + B(u,v)X_{v}## defined on a domain ##(u,v)## in the plane.
##X## is a three dimensional vector and ##A## and ##B## are arbitrary smooth functions.
When does such an equation determine a surface in ##R^3## and what in general can be said about the set of solutions?
Same question for ##X_{uu} = A(u,v)X_{u} + B(u,v)X_{v}##
##X_{uv} = A(u,v)X_{u} + B(u,v)X_{v}## defined on a domain ##(u,v)## in the plane.
##X## is a three dimensional vector and ##A## and ##B## are arbitrary smooth functions.
When does such an equation determine a surface in ##R^3## and what in general can be said about the set of solutions?
Same question for ##X_{uu} = A(u,v)X_{u} + B(u,v)X_{v}##