Geodesic completeness for Type~A surfaces
Preprint
Abstract
Type A surfaces are the locally homogeneous affine surfaces which can be locally described by constant Christoffel symbols. We address the issue of the geodesic completeness of these surfaces: we show that some models for Type A surfaces are geodesically complete, that some others admit an incomplete geodesic but model geodesically complete surfaces, and that there are also others which do not model any complete surface. Our main result provides a way of determining whether a given set of constant Christoffel symbols can model a complete surface.Keywords
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This publication has 10 references indexed in Scilit:
- Homogeneous affine surfaces: affine Killing vector fields and gradient Ricci solitonsJournal of the Mathematical Society of Japan, 2018
- Homogeneous affine surfaces: Moduli spacesJournal of Mathematical Analysis and Applications, 2016
- A classification of locally homogeneous affine connections on compact surfacesAnnals of Global Analysis and Geometry, 2014
- Locally homogeneous rigid geometric structures on surfacesGeometriae Dedicata, 2011
- Classification of locally homogeneous affine connections with arbitrary torsion on 2-dimensional manifoldsMonatshefte für Mathematik, 2007
- A note on the completeness of homogeneous quadratic vector fields on the planeQualitative Theory of Dynamical Systems, 2005
- A classification of locally homogeneous connections on 2-dimensional manifoldsDifferential Geometry and its Applications, 2004
- Locally homogeneous affine connections on compact surfacesProceedings of the American Mathematical Society, 2004
- On Locally Nonhomogeneous Pseudo–Riemannian Manifolds with Locally Homogeneous Levi–Civita ConnectionsInternational Journal of Mathematics, 2003
- A Classification of Locally Homogeneous Affine Connections with Skew-Symmetric Ricci Tensor on 2-Dimensional ManifoldsMonatshefte für Mathematik, 2000