Conformal geometry and its applications in differential equations

During my seminar I'd like to recall construction of local conformal invariant of metric in dimension n >= 3. In particular, the conformal flatness of metric is equivalent to vanishing of certain tensorial invariant. Then I will show how conformal invariants can be applied to differential equations. To a differential equation of certain type one can assign a conformal class of metric. Property of this metric can be translated to some property of the equation.