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, d...

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Bibliographic Details
Published in:	Ukrainian mathematical journal Vol. 67; no. 4; pp. 641 - 647
Main Author:	Altin, A
Format:	Journal Article
Language:	English
Published:	New York Springer US 01-09-2015 Springer
Subjects:	Algebra Analysis Applications of Mathematics Brief Communications Geometry Mathematics Mathematics and Statistics Statistics Riemannian Surface Local Parametrization Riemannian Manifold Tangent Space Circular Cylinder
Online Access:	Get full text
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Summary:	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.
ISSN:	0041-5995 1573-9376
DOI:	10.1007/s11253-015-1128-7