Abstract
One of the basic facts known in the theory of minimal Lagrangian surfaces is that a minimal Lagrangian surface of constant curvature in C 2 must be totally geodesic. In affine geometry the constancy of curvature corresponds to the local symmetry of a connection. In Opozda (Geom. Dedic. 121:155–166, 2006), we proposed an affine version of the theory of minimal Lagrangian submanifolds. In this paper we give a local classification of locally symmetric minimal affine Lagrangian surfaces in C 2. Only very few of surfaces obtained in the classification theorems are Lagrangian in the sense of metric (pseudo-Riemannian) geometry.
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Communicated by D. V. Alekseevsky.
The research supported by the KBN grant 1 PO3A 034 26.
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Opozda, B. Locally symmetric minimal affine Lagrangian surfaces in C2 . Monatsh Math 156, 357–370 (2009). https://doi.org/10.1007/s00605-008-0023-9
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DOI: https://doi.org/10.1007/s00605-008-0023-9