The energy of unit vector fields on odd-dimensional spheres is a functional that has a minimum in dimension 3 and an infimum in higher dimensions. Vector fields with isolated singularities arise naturally in the study of this functional. We consider the class of fields in S 3 having two antipodal singularities. We prove a lower bound, attained for the radial vector field, for the energy of this class of fields in terms of the indices of the singularities. A similar inequality is not to be expected in other dimensions.

Our main result in this paper establishes that if G is a compact Lie subgroup of the isometry group of a compact Riemannian manifold M acting with cohomogeneity one in M and either G has no singular orbits or the singular orbits of G have dimension at most n − 3, then the unit vector field N orthogonal to the principal orbits of G is weakly smooth and is a critical point of the energy functional acting on the unit normal vector fields of M. A formula for the energy of N in terms of the of integral of the Ricci curvature of M and of the integral of the square of the mean curvature of the principal orbits of G is obtained as well. In the case that M is the sphere and G the orthogonal group it is known that that N is minimizer. It is an open question if N is a minimizer in general.

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The anatomy and affinity of Triassic Argentinean conifer-like woods are reassessed, to provide information on the origin of derived conifers.

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