Department of Mathematics, University of Mary Washington, Fredericksburg, VA 22401, USA
Copyright © 2009 Yuan-Jen Chiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We generalize wave maps to biwave maps. We prove that the composition of a biwave map and a totally geodesic map is a biwave map. We give examples of biwave nonwave maps. We show that if is a biwave map into a Riemannian manifold under certain circumstance, then is a wave map. We verify that if is a stable biwave
map into a Riemannian manifold with positive constant sectional curvature satisfying the conservation law, then is a wave map. We finally obtain a theorem involving an unstable biwave map.