منابع مشابه
Two Examples of Affine Manifolds
An affine manifold is a manifold with a distinguished system of affine coordinates, namely, an open covering by charts which map homeomorphically onto open sets in an affine space E such that on overlapping charts the homeomorphisms differ by an affine automorphism of E. Some, but certainly not all, affine manifolds arise as quotients Ω/Γ of a domain in E by a discrete group Γ of affine transfo...
متن کاملAffine Anosov Diffeomorphims of Affine Manifolds
̂ M of the connection ∇M to the universal cover ̂ M of M is a locally flat connection. The affine structure of ̂ M is defined by a local diffeomorphism DM : ̂ M → R called the developing map. The developing map gives rise to a representation hM : π1 M → Aff R called the holonomy. The linear part L hM of hM is the linear holonomy. The affine manifold M,∇M is complete if and only if DM is a diffeomor...
متن کاملExamples of Manifolds
Definition 1 We now define what is meant by the statement that M is a d–dimensional manifold of class C (with 1 ≤ k ≤ ∞ — we shall deal almost exclusively with manifolds of class C). (a) Let M be a Hausdorff topological space. A coordinate system (or chart or coordinate patch) on M is a pair (U , φ) with U a connected open subset of M and φ a homeomorphism (a 1–1, onto, continuous function with...
متن کاملFlat Bundles on Affine Manifolds
We review some recent results in the theory of affine manifolds and bundles on them. Donaldson–Uhlenbeck–Yau type correspondences for flat vector bundles and principal bundles are shown. We also consider flat Higgs bundles and flat pairs on affine manifolds. A bijective correspondence between polystable flat Higgs bundles and solutions of the Yang–Mills–Higgs equation in the context of affine m...
متن کاملComplete affine manifolds: a survey
An affinely flat manifold (or just affine manifold) is a manifold with a distinguished coordinate atlas with locally affine coordinate changes. Equivalently M is a manifold equipped with an affine connection with vanishing curvature and torsion. A complete affine manifold M is a quotient E/Γ where Γ ⊂ Aff(E) is a discrete group of affine transformations acting properly on E. This is equivalent ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1981
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1981.94.327