Generalised connections and curvature
نویسندگان
چکیده
منابع مشابه
Generalised connections and curvature
The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a generalised connection. Some applications to singular solutions of Yang-Mills theory are given. Mathematics Subject Classification (2000): Primary: 46T30; secondary...
متن کاملCONNECTIONS, CURVATURE, AND p-CURVATURE
1.1. Connections and derivations. Let S be a scheme, and X smooth and finite type over S throughout. We have the rank-n vector bundle ΩX/S of 1-forms on X over S. We also fix some notation in the case that S is of characteristic p: in this case, we denote by FT the absolute Frobenius map for any scheme T , by X = X×S S the p-twist of X over S, where the map used in the fiber product is FS : S →...
متن کاملConnections and Curvature Notes
where Dvai is the directional derivative of the function ai in the direction v. Consequently we know when a vector field does not change along a curve γ: Dγ̇X = 0. Covariant derivatives generalize the directional derivatives allowing us to differentiate vector fields on arbitrary manifolds and, more generally, sections of arbitrary vector bundles. Definition 1.1 (Covariant derivative of sections...
متن کاملVector 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...
متن کاملRicci curvature of affine connections
We show various examples of torsion-free affine connections which preserve volume elements and have definite Ricci curvature tensors.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2005
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004105008649