Volume-minimizing Foliations on Spheres
نویسنده
چکیده
The volume of a k-dimensional foliation F in a Riemannian manifold Mn 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 the construction by Gluck and Ziller in [4], “singular” foliations by 3-spheres are constructed on round spheres S, as well as a singular foliation by 7-spheres on S, which minimize volume within their respective relative homology classes. These singular examples provide lower bounds for volumes of regular 3-dimensional foliations of S and regular 7-dimensional foliations of S.
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