In this talk, we extend the classical theory of minimal surfaces studied in Euclidean and Riemannian geometry to a more general framework in Weitzenböck and Riemann-Cartan geometry, which incorporates torsion. After providing a gentle introduction to minimal surface theory, we present theorems that generalize classical results concerning the holomorphic nature of the Hopf differential, the conformality of the Gauss map, and the minimality of surfaces.
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