Holonomy of flat affinely connected manifolds

DOI10.2307/2007104zbMath0065.37603OpenAlexW2312393834MaRDI QIDQ2653843

Louis Auslander, Lawrence Markus

Publication date: 1955

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2007104

zbMATH Keywords

Riemannian manifolds

Related Items (41)

Hereditary arithmetics ⋮ Lorentz spacetimes of constant curvature ⋮ Universal Lagrangian bundles ⋮ Flat affine symplectic Lie groups ⋮ The decomposition of a differentiable manifold and its applications ⋮ Flat affine manifolds and their transformations ⋮ Single basepoint subdivision schemes for manifold-valued data: time-symmetry without space-symmetry ⋮ On the Cohomology Groups of Real Lagrangians in Calabi–Yau Threefolds ⋮ Locality of relative symplectic cohomology for complete embeddings ⋮ Expanding maps, Anosov diffeomorphisms and affine structures on infra-nilmanifolds. ⋮ General relativity as a biconformal gauge theory ⋮ From almost (para)-complex structures to affine structures on Lie groups ⋮ A generalization of Bieberbach's theorem ⋮ Almost Lagrangian obstruction ⋮ Flat Affine, Projective and Conformal Structures on Manifolds: A Historical Perspective ⋮ On the Euler characteristic of compact complete locally affine spaces. II ⋮ A coordinate-free theory of virtual holonomic constraints ⋮ Integrable systems, symmetries, and quantization ⋮ On compact manifolds admitting indefinite metrics with parallel Weyl tensor ⋮ Symplectic torus actions with coisotropic principal orbits ⋮ Energy gap for Yang-Mills connections. II: Arbitrary closed Riemannian manifolds ⋮ Construction of finite braces ⋮ Complex product structures and affine foliations ⋮ Unnamed Item ⋮ Wave functions relative to a real polarization ⋮ The \(b\)-boundary of \(S^1\) with a constant connection ⋮ An Example of Almost Flat Affine Connections on the Three-Dimensional Sphere ⋮ The holonomy covering space in principal fibre bundles ⋮ Classification of cyclic braces, II ⋮ Locally Affine Spaces with Nilpotent Fundamental Groups ⋮ On Holonomy Covering Spaces ⋮ Unnamed Item ⋮ Affine geometric spaces in tangent categories ⋮ Invariante Grundlegung des affinen Raumes ⋮ Affine structures on a class of virtually nilpotent groups ⋮ Four Dimensional Compact Locally Hermitian Manifolds ⋮ Classical Differential Equations on Manifolds ⋮ Unnamed Item ⋮ The Radiance Obstruction and Parallel Forms on Affine Manifolds ⋮ The real cohomology of virtually nilpotent groups ⋮ Globally defined linear connections on the real line and the circle

This page was built for publication: Holonomy of flat affinely connected manifolds