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We consider surfaces on the pseudo-Helmholtz, proper Helmholtz, and dual Helmholtz Lie groups. These groups are united under the common term: Helmholtz-type groups. The Dirac, Weingarten, and Codazzi equations in the spinor representation are derived. The energy functional on these groups is studied.
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В. А. Кыров (2025) studied this question.
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