Olga Gil-Medrano

Second variation of volume and energy of vector fields. Stability of Hopf vector fields

Abstract. In this paper we compute the Hessian of the volume of unit vector fields at a minimal one. We also find the Hessians of a family of functionals thus generalizing the known results concerning second variation of the energy or total bending. We use them to study the stability of Hopf vector fields on n

Unit Vector Fields that are Critical Points of the Volume and of the Energy: Characterization and Examples

S^{2m+1}(r)

Harmonicity and minimality of oriented distributions

and to show that they are stable for n

Volume, energy and generalized energy of unit vector fields on Berger spheres: stability of Hopf vector fields

m=1

The Infimum of the Energy of Unit Vector Fields on Odd-Dimensional Spheres

, but that for n

GEODESICS ON SPACES OF ALMOST HERMITIAN STRUCTURES

m> 1

Area-minimizing vector fields on round 2-spheres

there is n

THE RIEMANNIAN MANIFOLD OF ALL RIEMANNIAN METRICS

r_0(m)le 1

Minimal unit vector fields

such that for n

Harmonic and minimal invariant unit vector fields on homogeneous Riemannian manifolds

r>r_0