Energy of Harmonic Maps and Gardiner’s Formula

Some geometrical properties of the oscillator group

‎We consider the oscillator group equipped with‎ ‎a biinvariant Lorentzian metric‎. ‎Some geometrical properties of this space and the harmonicity properties of left-invariant vector fields on this space are determined‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional‎ ‎restricted to vector fields‎. ‎Left-invariant vector fields defining harmonic maps are...

Regularity of Dirac-harmonic maps

For any n-dimensional compact spin Riemannian manifold M with a given spin structure and a spinor bundle ΣM , and any compact Riemannian manifold N , we show an ǫ-regularity theorem for weakly Dirac-harmonic maps (φ, ψ) : M ⊗ΣM → N ⊗ φ∗TN . As a consequence, any weakly Dirac-harmonic map is proven to be smooth when n = 2. A weak convergence theorem for approximate Dirac-harmonic maps is establi...

On the biharmonicity of product maps

where vg is the volume form on (M,g) and e( f )(x) := (1/2)‖df (x)‖T∗M⊗ f −1TN is the energy density of f at the point x ∈M. In local coordinates (x)i=1 on M and (y)a=1 on N , the energy density is given by e( f )(x)= (1/2)gi (x)hab( f (x))(∂ f a/∂xi)(∂ f b/∂x j). Critical points of the energy functional are called harmonic maps. The first variational formula of the energy gives the following c...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Harmonic maps, Bäcklund-Darboux transformations and ”line soliton” analogs

Harmonic maps from R2 or one-connected domain Ø ⊂ R2 into GL(m, C) and U(m) are treated. The GBDT version of the BäcklundDarboux transformation is applied to the case of the harmonic maps. A new general formula on the GBDT transformations of the Sym-Tafel immersions is derived. A class of the harmonic maps similar in certain ways to line-solitons is obtained explicitly and studied. MSC2000: 53C...