Displaying similar documents to “Harmonic and Minimal Unit Vector Fields on the Symmetric Spaces G 2 and G 2 / S O ( 4 ) ”

Harmonicity of vector fields on four-dimensional generalized symmetric spaces

Giovanni Calvaruso (2012)

Open Mathematics

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Let (M = G/H;g)denote a four-dimensional pseudo-Riemannian generalized symmetric space and g = m + h the corresponding decomposition of the Lie algebra g of G. We completely determine the harmonicity properties of vector fields belonging to m. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. Vector fields defining harmonic maps are also classified, and the energy of these vector fields is explicitly calculated. ...

Invariant harmonic unit vector fields on Lie groups

J. C. González-Dávila, L. Vanhecke (2002)

Bollettino dell'Unione Matematica Italiana

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We provide a new characterization of invariant harmonic unit vector fields on Lie groups endowed with a left-invariant metric. We use it to derive existence results and to construct new examples on Lie groups equipped with a bi-invariant metric, on three-dimensional Lie groups, on generalized Heisenberg groups, on Damek-Ricci spaces and on particular semi-direct products. In several cases a complete list of such vector fields is given. Furthermore, for a lot of the examples we determine...

On the intrinsic geometry of a unit vector field

Yampolsky, Alexander L. Yampolsky, Alexander L. (2002)

Commentationes Mathematicae Universitatis Carolinae

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We study the geometrical properties of a unit vector field on a Riemannian 2-manifold, considering the field as a local imbedding of the manifold into its tangent sphere bundle with the Sasaki metric. For the case of constant curvature K , we give a description of the totally geodesic unit vector fields for K = 0 and K = 1 and prove a non-existence result for K ≠ 0 , 1 . We also found a family ξ ω of vector fields on the hyperbolic 2-plane L 2 of curvature - c 2 which generate foliations on T 1 L 2 with leaves of constant...