A Generalized Frame Bundle for Certain Fréchet Vector Bundles and Linear Connections
نویسندگان
چکیده
منابع مشابه
Universal connections in Fréchet principal bundles
A new methodology leading to the construction of a universal connection for Fréchet principal bundles is proposed in this paper. The classical theory, applied successfully so far for finite dimensional and Banach modelled bundles, collapses within the framework of Fréchet manifolds. However, based on the replacement of the space of continuous linear mappings by an appropriate topological vector...
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 کاملNormal frames for linear connections in vector bundles and the equivalence principle in classical gauge theories
Frames normal for linear connections in vector bundles are defined and studied. In particular, such frames exist at every fixed point and/or along injective path. Inertial frames for gauge fields are introduced and on this ground the principle of equivalence for (system of) gauge fields is formulated. Bozhidar Z. Iliev: Normal frames, connections, gauge fields 1
متن کاملLagrangians and Euler morphisms on fibered - fibered frame bundles from projectable - projectable classical linear connections
We classify all FMm1,m2,n1,n2 -natural operators A transforming projectable-projectable torsion-free classical linear connections ∇ on fibered-fibered manifolds Y of dimension (m1,m2, n1, n2) into rth order Lagrangians A(∇) on the fibered-fibered linear frame bundle L(Y ) on Y . Moreover, we classify all FMm1,m2,n1,n2 -natural operators B transforming projectable-projectable torsion-free classi...
متن کاملStable Approximations of Certain Vector Bundles
0 −−−−→ O s −−−−→ E0 s∗ −−−−→ I −−−−→ 0. As usual, s is the distinguished nonzero global section of E0. The determinant line bundle of E0 is trivial, while the second Chern class is equal to the integer k. If X is in particular an algebraic surface, and H a fixed ample line bundle, then we can talk about slope-stability with respect to H. The bundle E0 is only slopesemistable, of slope 0, but t...
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: Tokyo Journal of Mathematics
سال: 1997
ISSN: 0387-3870
DOI: 10.3836/tjm/1270042405