Transversal biwave maps

In this paper, we prove that the composition of a transversal biwave map and a transversally totally geodesic map is a transversal biwave map.We show that there are biwave maps which are not transversal biwave maps, and there are transversal biwave maps which are not biwave maps either.We prove that if f is a transversal biwave map satisfying certain condition, then f is a transversal wave map.We finally study the transversal conservation laws of transversal biwave maps.