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The immersion of the string world sheet, regarded as a Riemann surface, in $R^3$ and $R^4$ is described by the generalized Gauss map. When the Gauss map is harmonic or equivalently for surfaces of constant mean curvature, we obtain Hitchins self-dual equations, by using $SO(3)$ and $SO(4)$ gauge fields constructed in our earlier studies. This complements our earlier result that $hsurd g = 1$ surfaces exhibit Virasaro symmetry. The self-dual system so obtained is compared with self-dual Chern-Simons system and a generalized Liouville equation involving extrinsic geometry is obtained. The immersion in $R^n, n>4$ is described by the generalized Gauss map. It is shown that when the Gauss map is harmonic, the mean curvature of the immersed surface is constant. $SO(n)$ gauge fields are constructed from the geometry of the surface and expressed in terms of the Gauss map. It is found Hitchins self- duality relations for the gauge group $SO(2)times SO(n-2)$.
Motivated by a class of near BPS Skyrme models introduced by Adam, Sanchez-Guillen and Wereszczynski, the following variant of the harmonic map problem is introduced: a map $phi:(M,g)rightarrow (N,h)$ between Riemannian manifolds is restricted harmon
$alpha$-Dirac-harmonic maps are variations of Dirac-harmonic maps, analogous to $alpha$-harmonic maps that were introduced by Sacks-Uhlenbeck to attack the existence problem for harmonic maps from surfaces. For $alpha >1$, the latter are known to sat
In this paper, we investigate representations of links that are either centrally symmetric in $mathbb{R}^3$ or antipodally symmetric in $mathbb{S}^3$. By using the notions of antipodally self-dual and antipodally symmetric maps, introduced and studie
We reconsider the renormalizability of topological Yang-Mills field theories in (anti-)self-dual Landau gauges. By employing algebraic renormalization techniques we show that there is only one independent renormalization. Moreover, due to the rich se
Higher Spin Gravities are scarce, but covariant actions for them are even scarcer. We construct covariant actions for contractions of Chiral Higher Spin Gravity that represent higher spin extensions of self-dual Yang-Mills and self-dual Gravity theor