Information om | Engelska ordet HOLONOMY

Exempel på hur man kan använda HOLONOMY i en mening

• In general, many elementary foliations give rise to monodromy and holonomy groupoids which are not Hausdorff.
• As a rule of thumb, it can occur whenever there are at least two parameters characterizing a wave in the vicinity of some sort of singularity or hole in the topology; two parameters are required because either the set of nonsingular states will not be simply connected, or there will be nonzero holonomy.
• In 1952 De Rham considered the converse, proving that, if there is a decomposition of the tangent bundle into vector subbundles which are invariant under the holonomy group, then the Riemannian structure must decompose as a product.
• A hyperkähler manifold is a Riemannian manifold whose holonomy group is contained in the symplectic group.
• In detail, if q ∈ P is another chosen basepoint for the holonomy, then there exists a unique g ∈ G such that q ~ p g (since, by assumption, M is path-connected).
• This fact immediately follows from the Bochner formula for holomorphic forms on a Kähler manifold, together the Berger classification of holonomy groups; ironically, it is often attributed to Bogomolov, who incorrectly went on to claim in the same paper that compact hyperkähler manifolds actually do not exist!.
• There is an interplay between these moduli spaces and the moduli spaces of principal bundles, vector bundles, Higgs bundles, and geometric structures on topological spaces, given generally by the observation that, at least locally, equivalent objects in these categories are parameterized by conjugacy classes of holonomy homomorphisms of flat connections.
• Actually, any isoparametric submanifold is foliated by the holonomy tubes of a submanifold with constant principal curvatures i.
• One of its first significant result, Reeb stability theorem, describes the local structure foliations around a compact leaf with finite holonomy group.
• This theorem was phrased in a new light in the work of Simon Donaldson in 1983, who showed that stable vector bundles correspond to Yang–Mills connections, whose holonomy gives the representations of the fundamental group of Narasimhan and Seshadri.
• He is mostly known for his work with Ludwig Faddeev on quantum anomalies, with Anton Alekseev on geometric methods in two-dimensional conformal field theories, for his work on background independent open string field theory, with Cumrun Vafa on superstrings and manifolds of exceptional holonomy, with Anton Gerasimov on tachyon condensation, with Andrei Losev, Nikita Nekrasov and Greg Moore on instantons and supersymmetric gauge theories, as well as for his work with Nikita Nekrasov on quantum integrable systems.
• This connection can have holonomy that obstructs the existence of "global" twistors (that is, solutions of the twistor equation in open sets).
• He constructed instanton solutions on coset manifolds and cones thereover with special holonomy and extended them to flux vacua of the heterotic string.

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