I have encountered a more general definition of a connection for vector bundles (Vector Bundles with a Connection, S.S Chern) where the connection is given by D:Γ(E)→Γ(T∗M⊗E), where Γ(∗) denotes the vector space of sections of ∗,D:Γ(E)→Γ(T∗M⊗E), where ...
We prove that smooth 1-dimensional topological field theories over a manifold are the same as vector bundles with connection. The main novelty is our definition of the smooth 1-dimensional bordism category, which encodes cutting laws rather than gluing laws. We make this idea precise through a ...
In particular we look at the case of complex algebraic varieties where we can compare with the complex analytic category. Finally we study vector bundles with a connection where stronger results can be achieved.doi:10.48550/arXiv.1106.3969Helmut A. Hamm...
英文: The Total Stiefel-Whitney Classes of Vector Bundles on RP(j)×CP(k)中文: RP(j)×CP(k)上向量丛的全Stiefel-Whitney类 英文: Study of Fluidelastic Instability in Tube Bundles中文: 管束的流体弹性不稳定性的研究 英文: Poisson Structures on Fibre Bundles中文: 纤维丛上的Poisson结构 ...
Let E→ME→M be a Riemannian vector bundle over an oriented Riemannian manifold (M,g)(M,g) with a connection ∇∇. Let Γ(E)Γ(E) denote the vector space of sections of E→ME→M. For σ∈Γ(E)σ∈Γ(E), its Sobolev kk-norm (k=1,2,…)(k=1,2,…) is defined ...
Finsler vector bundles -- Metrizable connections As a corollary a metrizability condition for any linear connection in the Finsler vector bundle ξ is provided.doi:10.1023/B:MAHU.0000038968.31593.ceMihai... M Anastasiei - 《Periodica Mathematica Hungarica》 被引量: 14发表: 2004年 Geometric phase...
This example is from Wikipedia and may be reused under a CC BY-SA license. More generally, differential geometers consider spaces with a vectorbundle and an arbitrary affine connection which is not defined in terms of a metric. From Wikipedia This example is from Wikipedia and may be reuse...
Definition 7.5. 令\pi_{E}: E \rightarrow M 和\pi_{F}: F \rightarrow N 是C^\infty vector bundles。一个从 E 到F 的C^\infty bundle map 是一对 C^\infty 映射(\varphi: E \rightarrow F, \underline{\varphi}: M \rightarrow N) s.t. ...
Let $X$ be a proper smooth algebraic variety over a field $k$ of characteristic zero and let $D$ be a divisor with simple normal crossings. Let $M$ be a vector bundle over $X-D$ equipped with a flat connection with possible irregular singularities along $D$. We define a cleanliness ...