Surfaces on Helmholtz-type groups

V. A. Kyrov

Gorno-Altaisk State University, Gorno-Altaisk, Russia

Abstract: 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.

Keywords: Lie group, surface in a Lie group, proper Helmholtz group, pseudo-Helmholtz group, dual Helmholtz group, Dirac equation, Weingarten equation, Codazzi equation.

UDC: 514.765

MSC: 35R30

Received: 17.02.2025
Revised: 17.05.2025
Accepted: 25.06.2025

DOI: 10.33048/smzh.2025.66.511

 English version: Siberian Mathematical Journal, 2025, 66:5, 1218–1230