Un analogue conforme des applications harmoniques

Abstract

On a Riemannian surface, the energy of a map into a Riemannian manifold is a conformal invariant functional, and its critical points are the harmonic maps. Our main result is a generalization of this theorem when the starting manifold is even dimensional. We then build a conformal invariant functional for the maps between two Riemannian manifolds. Its critical points then called C-harmonic are the solutions of a nonlinear elliptic PDE of order n, which is conformal invariant with respect to the start manifold. For the trivial case of real or complex functions of M, we find again the GJMS operator, with a leading part power to the n / 2 of the Laplacian. To cite this article: V. Bérard, C. R. Acad. Sci. Paris, Ser. I 346 (2008).