Biwave Maps into Manifolds

Biwave Maps into Manifolds

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 f is a biwave map into a Riemannian manifold under certain circumstance, then f is a wave map. We verify that if f is a stable biwave map into a Riemannian manifold with positive constant sectional curvature sa...

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 ma...

Quasiconformal Harmonic Maps into Negatively Curved Manifolds

Let F : M → N be a harmonic map between complete Riemannian manifolds. Assume that N is simply connected with sectional curvature bounded between two negative constants. If F is a quasiconformal harmonic diffeomorphism, then M supports an infinite dimensional space of bounded harmonic functions. On the other hand, if M supports no non-constant bounded harmonic functions, then any harmonic map o...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Cobordisms of Fold Maps of 4-manifolds into the Space

We compute the oriented cobordism group of fold maps of 4-manifolds into R 3 with all the possible restrictions (and also with no restriction) to the singular fibers. We also give geometric invariants which describe completely the cobordism group of fold maps.