Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 20 for “"holonomy"”.
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On imbeddings and holonomy
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1959.
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Deformations and gluing of asymptotically cylindrical manifolds with exceptional holonomy
In Berger's classification of Riemannian holonomy groups there are several infinite families and two exceptional cases: the groups Spin(7) and G_2. This thesis is mainly concerned with 7-dimensional manifolds with holonomy G_2. A metric with holonomy contained in G_2 can be defined in terms of a …
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Distribution of Holonomy about Closed Geodesics on Compact Hyperbolic 3-Manifolds
… geodesics are parametrized by their length and holonomy, which describes the angle of rotation by parallel transport about the geodesic. First, we prove ambient prime geodesic theorems, which provide an asymptotic count of closed geodesics by their length and holonomy and imply e ective …
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Cyclic universes & direct detection of cosmic expansion by holonomy in the McVittie spacetime
… to Directly Detect Cosmic Expansion by Holonomy. Two thought experiments are proposed to directly measure the expansion of the universe by the parallel transfer of a vector around a closed loop in a curved spacetime. Generally, expansion would cause a measurable deficit angle between the …
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Symplectic and complex foliations
… the Darboux theorem may be established, basic (holonomy invariant) functions may be regarded as transverse Hamiltonian functions for which Hamiltonian ""vector fields"" are holonomy invariant classes of vector fields in the transverse bundle, and this structure induces a holonomy invariant …
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The Fundamental Group: A Geometric Perspective
… through the lens of parallel transport and the holonomy group. We establish a surjective homomorphism from the fundamental group to the quotient of the full holonomy group by the restricted holonomy group, demonstrating how the global topological features of a manifold strictly govern the …
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Geometry of Spaces of Planar Quadrilaterals
… space of paths in the moduli space can exhibit holonomy. We determine exactly which collections of side lengths allow holonomy.
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Soft Hair and Subregions in Quantum Gravity
… by measuring an object known as ‘Uhlmann holonomy’ on the boundary, which is a generalisation of Berry phase. The Uhlmann holonomy is actually a direct measure of the entanglement in the quantum state, and so this provides a connection between edge modes and entanglement. In the final part …
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Calibrations and minimal Lagrangian submanifolds
… manifolds. 4) A Riemannian 7-manifold with holonomy G2. We will construct some new examples of coassociative submanifolds on complete Riemannian 7-manifolds with holonomy G2 via group actions.
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Anti-self-dual fields and manifolds
… dimensions on manifolds of special Riemannian holonomy, among these hyper–Kähler, Quaternion–Kähler and Spin(7)–manifolds. We first consider the octonionic anti–self–duality equations on manifolds with holonomy Spin(7). We construct explicit solutions to their symmetry reductions, the …
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Deformations of Cayley submanifolds
… Spin(7). If this 4-form Phi is closed, then the holonomy of M is contained in Spin(7) and Cayley submanifolds are calibrated minimal submanifolds. McLean studied the deformations of closed Cayley submanifolds. The deformation problem is elliptic but in general obstructed. We show that for a …
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Geometry and Topology of Quantum States in Quasicrystalline Systems
… we also discover a so-called spiral holonomy in the effective band structure, in which circular trajectories result in evolution into an orthogonal state. We show that this feature is a result of the pseudo-Brillouin-zone possessing the topology of a higher genus torus. We then …
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Orderability of homology spheres obtained by Dehn filling
… representations, I construct the holonomy extension locus of a $\mathbb{Q}$-homology solid torus which is an analog of its translation extension locus. Using extension loci, I study $\mathbb{Q}$-homology 3-spheres coming from Dehn fillings of $\mathbb{Q}$-homology solid tori and …
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Foliations and exotic index theory
… on compact manifolds, the corona of the holonomy groupoid is a fiber bundle over the ambient manifold whose fiber is the corona of the universal leaf. By this property, an idea in the work of S. Hurder can be applied to Riemannian foliations on a compact manifold to show that the analytic …
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Confinement and Chiral Phase Transitions in SU(2) Gauge Theory via Topological Objects
… finite-temperature instantons with non-trivial holonomy. I present a comprehensive numerical study of the confining properties in SU(2) Yang-Mills theory at finite temperature, obtaining important observables which are then compared with available data from state of the art simulations of …
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Cohomology Jumping Loci and the Relative Malcev Completion
… p is the trivial representation, then u_p is the holonomy Lie algebra, which is well-known to be quadratically presented. In contrast, we show that when X is the complement of the braid arrangement in complex two-space, there are infinitely many representations p from G into (C^*)^2 for which u_p …
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Differential systems, moving frames, structure-preserving submersions and geometrical problems in physics
… relativity, based on Riemannian geometry with a holonomy constraint, and thus argue that such a theory is not a suitable candidate for a physical theory. As for structure-preserving submersions, which we propose as a generalisation for Riemannian submersions to other geometrical structures, after …
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Deformation theory of Cayley submanifolds
Cayley submanifolds are naturally arising volume minimising submanifolds of $Spin(7)$- manifolds. In the special case that the ambient manifold is a four-dimensional Calabi--Yau manifold, a Cayley submanifold might be a complex surface, a special Lagrangian submanifold or neither. In this thesis, …
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Geometric properties of the Bismut and the Obata connections
L'abstract è presente nell'allegato / the abstract is in the attachment
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Reconstruction of deligne classes and cocycles
In der vorliegenden Arbeit verallgemeinern wir im Wesentlichen zwei Theoreme von Mackaay-Picken und Picken (2002, 2004). Im ihrem Artikel zeigen Mackaay und Picken,dass es eine bijektive Korrespodenz zwischen Deligne 2-Klassen $\xi \in \check{H}^2(M, \mathcal{D}^2)$ und Holonomie Abbildungen von …