The geometry of locally symmetric affine surfaces
Differential Geometry
2017-06-19 v1 General Relativity and Quantum Cosmology
Abstract
We examine the local geometry of affine surfaces which are locally symmetric. There are 6 non-isomorphic local geometries. We realize these examples as Type A, Type B, and Type 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.
Keywords
Cite
@article{arxiv.1706.04958,
title = {The geometry of locally symmetric affine surfaces},
author = {D. D'Ascanio and P. Gilkey and P. Pisani},
journal= {arXiv preprint arXiv:1706.04958},
year = {2017}
}