2018•arXiv (Cornell University)Open access

Affine Killing complete and geodesically complete homogeneous affine surfaces

Peter Gilkey, JeongHyeong Park, X. Valle-Regueiro

Abstract

An affine manifold is said to be geodesically complete if all affine geodesics extend for all time. It is said to be affine Killing complete if the integral curves for any affine Killing vector field extend for all time. We use the solution space of the quasi-Einstein equation to examine these concepts in the setting of homogeneous affine surfaces.

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Key concepts: Affine coordinate system, Affine transformation, Affine plane (incidence geometry), Affine geometry of curves, Affine group, Affine hull, Affine combination, Geodesic