Connections on 2-osculator bundles of infinite dimensional manifolds
نویسندگان
چکیده
The geometry of the second order osculating bundle OscM , is in many cases determined by its spray and the associated nonlinear connection. For a Banach manifold M , we firstly endow OscM with a fiber bundle structure over M . Three different concepts which are used in many finite dimensional literatures, that is the horizontal distributions, nonlinear connections and sprays are studied in detail and their close interaction is revealed. Moreover we propose a special lift for a connection on the base manifold to OscM . M.S.C. 2010: 58A05; 58B20.
منابع مشابه
Principal Bundles over Statistical Manifolds
In this paper, we introduce the concept of principal bundles on statistical manifolds. After necessary preliminaries on information geometry and principal bundles on manifolds, we study the α-structure of frame bundles over statistical manifolds with respect to α-connections, by giving geometric structures. The manifold of one-dimensional normal distributions appears in the end as an applicatio...
متن کاملChern–weil Theory for Certain Infinite-dimensional Lie Groups
Chern–Weil and Chern–Simons theory extend to certain infinite-rank bundles that appear in mathematical physics. We discuss what is known of the invariant theory of the corresponding infinite-dimensional Lie groups. We use these techniques to detect cohomology classes for spaces of maps between manifolds and for diffeomorphism groups of manifolds.
متن کاملSome recent work in Fréchet geometry
Some recent work in Fréchet geometry is briefly reviewed. In particular an earlier result on the structure of second tangent bundles in the finite dimensional case was extended to infinite dimensional Banach manifolds and Fréchet manifolds that could be represented as projective limits of Banach manifolds. This led to further results concerning the characterization of second tangent bundles and...
متن کاملOn Ricci identities for submanifolds in the 2-osculator bundle
It is the purpose of the present paper to outline an introduction in theory of embeddings in the 2-osculator bundle. First, we recall the notion of 2-osculator bundle ([1],[2]) and the notion of submanifolds in the 2-osculator bundle. A moving frame is constructed. The induced connections and the relative covariant derivation are discussed in third and fourth sections.The Ricci identities for t...
متن کاملUnstable Bundles in Quantum Field Theory
The relation between connections on 2-dimensional manifolds and holomorphic bundles provides a new perspective on the role of classical gauge fields in quantum field theory in two, three and four dimensions. In particular we show that there is a close relation between unstable bundles and monopoles, sphalerons and instantons. Some of these classical configurations emerge as nodes of quantum vac...
متن کامل