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On the energy of unit vector fields with isolated singularities

100%

Brito F. G. B., Walczak P. G.

Annales Polonici Mathematici

2000

tom 73

nr 3

269-274

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').

Harmonic conformal flows on manifolds of constant curvature

63%

Fawaz A.

Open Mathematics

2007

tom 5

nr 3

493-504

We compute the energy of conformal flows on Riemannian manifolds and we prove that conformal flows on manifolds of constant curvature are critical if and only if they are isometric.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Open Mathematics

1 Brito F. G. B.

1 Fawaz A.

1 Walczak P. G.

1 2007

1 2000

Wyniki wyszukiwania

On the energy of unit vector fields with isolated singularities

Harmonic conformal flows on manifolds of constant curvature