Discontinuous Normals in Non-Euclidean Geometries and Two-Dimensional Gravity

  title={Discontinuous Normals in Non-Euclidean Geometries and Two-Dimensional Gravity},
  author={Emmanuele Battista and Giampiero Esposito},
This paper builds two detailed examples of generalized normal in non-Euclidean spaces, i.e., the hyperbolic and elliptic geometries. In the hyperbolic plane we define a n-sided hyperbolic polygon P, which is the Euclidean closure of the hyperbolic plane H, bounded by n hyperbolic geodesic segments. The polygon P is built by considering the unique geodesic that connects the n+2 vertices z˜,z0,z1,...,zn−1,zn. The geodesics that link the vertices are Euclidean semicircles centred on the real axis… 

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