Resumen de Descending maps between slashed tangent bundles

I. Bucataru, M. F. Dahl

• Suppose T \ {0} and TM \ {0} are slashed tangent bundles of smooth manifolds M and fM, respectively. In this paper we first give a differential-topological characterization of those diffeomorphisms F : TM \ {0} --> TM \ {0} that can be written as F = (D.)j TMn0 for a diffeomorphism . : M ! fM. When this is the case we say that F descends. Using the characterization we obtain two geometric results. First, if M is equipped with two sprays, we obtain sufficient conditions that imply that F descends to a totally geodesic map. Second, if M has two Riemann metrics, we obtain sufficient conditions for F to descend to an isometry.