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The geometry of locally symmetric affine surfaces. (English) Zbl 1414.53029
Summary: We examine the local geometry of affine surfaces which are locally symmetric. There are six non-isomorphic local geometries. We realize these examples as type \(\mathcal {A}\), type \(\mathcal {B}\), and type \(\mathcal {C}\) geometries using a result of Opozda and classify the relevant geometries up to linear isomorphism. We examine the geodesic structures in this context. Particular attention is paid to the Lorentzian analogue of the hyperbolic plane and to the pseudosphere.

MSC:
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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