Harmonic Maps and Gravitating Monopoles and Skyrmions * Yves Brihaye † Facult´ e des Sciences, Universit´ e de Mons-Hainaut, 7000 Mons, Belgium Betti Hartmann ‡ School of Engineering and Sciences, IUB, 28725 Bremen, Germany Theodora Ioannidou § Maths Division, School of Technology, University of Thessaloniki, Thessaloniki 54124, Greece Wojtek J. Zakrzewski ¶ Department of Mathematical Sciences , University of Durham Durham DH1 3LE , United Kingdom October 18, 2004 Abstract We present some results of our recent work [1] on the solutions of the SU (N ) Einstein-Skyrme system. In this work we expressed the chiral fields (which were not simple embeddings of the SU (2) one) in terms of 2 dimensional S 2 → S 2 harmonic maps. This has allowed us * Talk given by W. J. Zakrzewski † yves.brihaye@umh.ac.be ‡ b.hartmann@iu-bremen.de § ti3@auth.gr ¶ w.j.zakrzewski@durham.ac.uk