A theorem about energy and volume of vector fields with the "proportional volume property"

作者：Brito Fabiano G; Gomes Andre O^*; Mesquita Robson M

来源：Journal of Geometry and Physics, 2016, 100: 96-100.

DOI：10.1016/j.geomphys.2015.11.003

• Hopf flows
• Vector fields
• Volume and energy

In this paper, we define a certain proportional volume property for a unit vector field on a spherical domain in S-3. 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.

• 出版日期2016-2