Article ID Journal Published Year Pages File Type
1894621 Journal of Geometry and Physics 2016 5 Pages PDF
Abstract
In this paper, we define a certain proportional volume property for a unit vector field on a spherical domain in S3. We prove that the volume of these vector fields has an absolute minimum, and that this value is equal to the volume of the Hopf vector field. Some examples of such vector fields are given. We also study the minimum energy of solenoidal vector fields which coincides with a Hopf flow along the boundary of a spherical domain of S2k+1.
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Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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