The Energy of a Domain on the Surface
We compute the energy of a unit normal vector field on a Riemannian surface M. It is shown that the energy of the unit normal vector field is independent of the choice of an orthogonal basis in the tangent space. We also define the energy of the surface. Moreover, we compute the energy of spheres, domains on a right circular cylinder and torus, and of the general surfaces of revolution.
English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 4, pp 641-647.
Citation Example: Altin A. The Energy of a Domain on the Surface // Ukr. Mat. Zh. - 2015. - 67, № 4. - pp. 568-573.