Volume-minimizing foliations on spheres

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dc.creatorBrito, Fabiano
dc.creatorJohnson, David L.
dc.date2004-02-18
dc.date.accessioned2026-07-07T05:05:33Z
dc.date.available2026-07-07T05:05:33Z
dc.descriptionThe volume of a k-dimensional foliation $\mathcal{F}$ in a Riemannian manifold $M^{n}$ is defined as the mass of image of the Gauss map, which is a map from M to the Grassmann bundle of k-planes in the tangent bundle. Generalizing a construction by Gluck and Ziller, "singular" foliations by 3-spheres are constructed on round spheres $S^{4n+3}$, as well as a singular foliation by 7-spheres on $S^{15}$, which minimize volume within their respective relative homology classes. These singular examples provide lower bounds for volumes of regular 3-dimensional foliations of $S^{4n+3}$ and regular 7-dimensional foliations of $S^{15}$ .
dc.description12 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/0402294
dc.identifierhttp://arxiv.org/abs/math/0402294
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70204
dc.subjectDifferential Geometry
dc.subject53C12, 53C38
dc.titleVolume-minimizing foliations on spheres
dc.typetext

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