Gauss maps and duality of sphere bundles
Given a sphere bundle, we define a Gauss map of the bundle, and from this we define an orthogonal sphere bundle. We define the dual of a Gauss map, and show that it is equal to either the orthogonal bundle or the singularity set of the orthogonal bundle’s Gauss map. This is a direct generalization of the case where the bundles are the unit tangent and unit normal bundles of an immersed manifold. The theory is supported by several examples. We end with looking at the duals of certain submanifolds of the sphere bundle.
Digital Object Identifier (DOI)
Dreibelbis, D. (2016). Gauss maps and duality of sphere bundles. Contemporary Mathematics, 675, 77-88.