Abstract:The volume of a k-dimensional foliation F in a Riemannian manifold M n is defined as the mass of the image of the Gauss map, which is a map from M to the Grassmann bundle of k-planes in the tangent bundle. Generalizing the construction by Gluck and Ziller (Comment. Math. Helv. 61 (1986), 177-192), 'singular' foliations by 3-spheres are constructed on round spheres S 4nþ3 , as well as a singular foliation by 7-spheres on S 15 , which minimize volume within their respective relative homology classes. These singu… Show more
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.