General connections on vector bundles
نویسندگان
چکیده
منابع مشابه
Vector Bundles, Connections and Curvature
Definition 1. Let M be a differentiable manifold. A C∞ complex vector bundle consists of a family {Ex}x∈M of complex vector spaces parametrized by M , together with a C∞ manifold structure of E = ∪x∈MEx such that 1. The projection map π : E →M taking Ex to x is C∞, and 2. For every x0 ∈M , there exists an open set U inM containing x0 and a diffeomorphism φU : π −1(U)→ U × C taking a vector spac...
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−→ V, (v1, v2) −→ v1+v2, are smooth. Note that we can add v1, v2∈V only if they lie in the same fiber over M , i.e. π(v1)=π(v2) ⇐⇒ (v1, v2) ∈ V ×M V. The space V ×M V is a smooth submanifold of V ×V , as follows immediately from the Implicit Function Theorem or can be seen directly. The local triviality condition means that for every point m∈M there exist a neighborhood U of m in M and a diffeo...
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ژورنال
عنوان ژورنال: Kodai Mathematical Journal
سال: 1985
ISSN: 0386-5991
DOI: 10.2996/kmj/1138037100