The elliptic system of equations, which is general-covariant and locallySU(2)-covariant, is investigated. The new condition of the Dirichlet problemsolvability and the condition of zeros absence for solutions are obtained forthis system, which contains in particular case the Sen-Witten equation. On thisbasis it is proved the existence of the wide class of hypersurfaces, in allpoints of which there exists a correspondence between the Sen-Witten spinorfield and three-frame, which generalizes the Nester orthoframe. The Nesterspecial orthoframe also exists on a certain subclass containing not only themaximal hypersurfaces.
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