Geodesic Connectedness of Affine Manifolds

2020/04/17 by Ivan P. Costa e Silva, Silva, Ivan P. Costa e, José Luis Flores +1 · 1 citation
Mathematics · #53C22 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2004.08357

openalex publication_date 2020/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss new sufficient conditions under which an affine manifold (M,∇) is geodesically connected. These conditions are shown to be essentially weaker than those discussed in groundbreaking work by Beem and Parker and in recent work by Alexander and Karr, with the added advantage that they yield an elementary proof of the main result.

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