Resumen de A characterization of revolution quadrics by a system of partial differential equations

Vladimir Oliker

• It is shown that existence of a global solution to a particular nonlinear system of second order partial differential equations on a complete connected Riemannian manifold has topological and geometric implications and that in the domain of positivity of such a solution, its reciprocal is the radial function of only one of the following rotationally symmetric hypersurfaces in : paraboloid, ellipsoid, one sheet of a two-sheeted hyperboloid, and a hyperplane.