2001/05/22 by Aristide Tsemo, A. Tsemo, Tsemo, A.
Mathematics · #53C15 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:53C15
paper · pdf · doi:10.48550/arxiv.math/0105179
26 pages, To be published in the Michigan Mathematical Journal
arxiv created 2001/05/22 · openalex publication_date 2001/05/22 · arxiv updated 2009/11/30 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We study affine maps between affine manifolds. Even when the fibers are compact and diffeomorphic, two of them can inherit different affine structures from the source space. This leads to a fixed linear holonomy deformation theory of the affine structure of an affine manifold. We found various conditions which make the fibers to be affinely isomorphic. We also classify affine bundles which total space is a compact and complete affine manifold.