Geodesic
Hyperk\"ahler Manifolds and Seiberg--Witten Equations
Informatics and Automation, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 263-276.

Voir la notice de l'article provenant de la source Math-Net.Ru

The mathematical properties of the so-called gauged nonlinear $\sigma$-model in dimension 4 are studied. An important element of the construction is a nonlinear generalization of the Dirac operator on a 4-manifold such that the fiber of the spinor vector bundle, a copy of quaternions $\mathbb H$, is replaced by a hyperkähler manifold endowed with a hyperkähler Lie group action and an additional symmetry. This Dirac operator is used to define Seiberg–Witten moduli spaces. An explicit Weitzenböck formula for such a Dirac operator is derived and applied to describe some properties of the Seiberg–Witten moduli spaces. 
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V. Ya. Pidstrigach. Hyperk\"ahler Manifolds and Seiberg--Witten Equations. Informatics and Automation, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 263-276. http://geodesic.mathdoc.fr/item/TRSPY_2004_246_a17/

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