The Geometry of Locally Symmetric Affine Surfaces

  • D. D’Ascanio
  • P. Gilkey
  • P. Pisani


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.


Ricci tensor Symmetric affine surface Geodesic completeness 

Mathematics Subject Classification (2010)




Research partially supported by project MTM2016-75897-P (Spain).


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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Instituto de Física La Plata, CONICET and Departamento de Física, Facultad de Ciencias ExactasUniversidad Nacional de La PlataLa PlataArgentina
  2. 2.Mathematics DepartmentUniversity of OregonEugeneUSA

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