ArticleOriginal scientific text
Title
On the energy of unit vector fields with isolated singularities
Authors 1, 2
Affiliations
- Departamento de Matemática-IME-USP, Caixa Postal 66281-CEP 05315-970, São Paulo-SP, Brazil
- Department of Mathematics, Łódź University, Banacha 22, 90-238 Łódź, Poland
Abstract
We consider the energy of a unit vector field defined on a compact Riemannian manifold M except at finitely many points. We obtain an estimate of the energy from below which appears to be sharp when M is a sphere of dimension >3. In this case, the minimum of energy is attained if and only if the vector field is totally geodesic with two singularities situated at two antipodal points (at the 'south and north pole').
Keywords
Ricci curvature, vector field, mean curvature, energy
Bibliography
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- P. G. Walczak, An integral formula for a Riemannian manifold with two orthogonal complementary distributions, Colloq. Math. 58 (1990), 243-252.
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- G. Wiegmink, Total bending of vector fields on the sphere
- C. M. Wood, On the energy of a unit vector field, Geom. Dedicata 64 (1997), 319-330.
Pages:
269-274
Main language of publication
English
Received
1999-11-17
Published
2000
Exact and natural sciences