We describe a simple fundamental domain for the holonomy group of the boundary unipotent spherical CR uniformization of the figure eight knot complement, and deduce that small deformations of that holonomy group (such that the boundary holonomy remains parabolic) also give a uniformization of the figure eight knot comp…
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48 results for “Holonomy parameters”
The study reveals a persistent bias in the distribution of holonomy on compact hyperbolic 3-manifolds.
problem The distribution of holonomy on compact hyperbolic 3-manifolds is not uniformly distributed.
method An asymptotic count of closed geodesics by their length and holonomy, and analysis of spectral parameters.
result A normalized, smoothed bias count of holonomy is distributed according to a probability distribution, controlled by the number of zero spectral parameters.
This paper calculates the derivative of surface holonomy for non-abelian gerbes.
problem Calculating the derivative of surface holonomy for non-abelian gerbes.
method Explicit calculation of the derivative formula for surface holonomy of squares mapped into the base manifold.
result Derivation of a formula for the derivative of surface holonomy of squares mapped into the base manifold.
Non-compact G_2 holonomy metrics that arise from a T^2 bundle over a hyper-Kahler space are discussed. These are one parameter deformations of the metrics studied by Gibbons, Lu, Pope and Stelle in hep-th/0108191. Seven-dimensional spaces with G_2 holonomy fibered over the Taub-Nut and the Eguchi-Hanson gravitational i…
Constructing solutions to the heterotic G system on specific types of manifolds.
problem Finding solutions to the heterotic G system on certain types of manifolds.
method Investigating a 1-parameter family of G-connections on tangent bundles.
result Obtaining several approximate and one new class of exact solutions on degenerate 3--Sasaki manifolds.
G2-manifolds with a cohomogeneity-one action of a compact Lie group G are studied. For G simple, all solutions with holonomy G2 and weak holonomy G2 are classified. The holonomy G2 solutions are necessarily Ricci-flat and there is a one-parameter family with SU(3)-symmetry. The weak holonomy G2 solutions are Einstein o…
Reflection Symmetry, APS Boundary Conditions, and Equivariant Spectral Flow on a Warped Cylindermath-ph
Study reflection symmetry and APS boundary conditions on a warped cylinder.
problem Analyzing reflection symmetry and APS boundary conditions for twisted Dirac operators on a finite warped cylinder.
method Examined reflection symmetry and APS boundary conditions for twisted Dirac operators on a finite warped cylinder, considering both fixed and varying holonomy.
result Reflection symmetry lifts to a unitary symmetry under specific conditions, and the spectral flow admits an RO(O(2))-valued decomposition for fixed holonomy.
Researchers study the conformal geometry of bivariate Gaussian manifolds.
problem Exploring the conformal structure of Fisher-Rao metric on statistical manifolds.
method Determined invariants of the conformal structure of the Fisher-Rao metric on the bivariate Gaussian manifold.
result The conformal holonomy group is for generic random variables, but for independent ones.
New transitions found in Spin(7) holonomy metrics related to a dynamical system.
problem Understanding the geometry of Spin(7) holonomy metrics with Aloff--Wallach spaces.
method Relating Spin(7)-equations to a 3-dimensional dynamical system.
result Discovered new transitions with Spin(7) holonomy metrics.
We study the existence of invariant metrics with holonomy on compact nilmanifolds, i.e. on compact quotients of nilpotent Lie groups by discrete subgroups. We prove that, up to isomorphism, there exists only one indecomposable nilpotent Lie algebra admitting a torsion-free -stru…
A torsion-free G_2 structure admitting an infinitesimal isometry is shown to give rise to a 4-manifold equipped with a complex symplectic structure and a 1-parameter family of functions and 2-forms linked by second order equations. Reversing the process in various special cases leads to the construction of explicit met…
Classifies foliations with a hypersurface as the singular leaf and open leaves.
problem Classifying foliations with a hypersurface as the singular leaf and open leaves.
method Analyzes the transverse order k foliations, showing that a loop in the singular leaf induces a well-defined holonomy transformation.
result A complete classification of these foliations and concrete descriptions of their associated groupoids and algebras.
New metric tensor field on symmetric matrices simplifies eigenvector computation.
problem Complex eigenvector computation for 2x2 symmetric matrices.
method Introducing a metric tensor field on the space of symmetric matrices, resulting in a curved manifold.
result Parallel transport simplifies eigenvector computation for one-parameter families of matrices.
We investigate the Lawson genus surface by methods from integrable system theory. We prove that the associated family of flat connections comes from a family of flat connections on a punctured sphere. We describe the symmetries of the holonomy and show that it is already determined by the holonomy around one of…
This paper studies the relation between two notions of holonomy on a conformal manifold. The first is the conformal holonomy, defined to be the holonomy of the normal tractor connection. The second is the holonomy of the Fefferman-Graham ambient metric of the conformal manifold. It is shown that the infinitesimal confo…
We study supergravity solutions corresponding to fivebranes wrapped on a three-sphere inside a G_2 holonomy manifold. By changing a parameter the solutions interpolate between a G_2 manifold X_i \cong S^3 x R^4 with flux on a three-sphere and a distinct G_2 manifold X_j \cong S^3 x R^4 with branes on another three-sphe…
New -holonomy manifolds from 5d N=1 theories domain walls.
problem Geometrizing domain walls in 5d N=1 theories.
method Constructing 7-manifolds by fibering a Calabi-Yau over a real line.
result 7-manifolds with -holonomy from domain walls in 5d theories.
Holonomy of Weyl connections in Lorentzian space classified.
problem Classifying holonomy algebras of Weyl connections in Lorentzian signature.
method Classification through construction of examples of Weyl connections with all possible holonomy algebras.
result Examples of Weyl connections with all possible holonomy algebras constructed.
New method for foliated bundles using holonomy groupoids.
problem Constructing holonomy groupoids for foliated bundles.
method Partial connection on diffeological principal bundle of germs.
result New hierarchy of holonomy groupoids for foliated bundles.
Holonomy groups of metric connections converge in a monotonic way.
problem Monotonicity of holonomy groups under convergence of metric connections.
method Proving the monotonicity of holonomy groups for sequences of metric connections converging in .
result The holonomy group of the limit connection is contained in the holonomy group of the initial connections.
The problem of classification of connected holonomy groups (equivalently of holonomy algebras) for pseudo-Riemannian manifolds is open. The classification of Riemannian holonomy algebras is a classical result. The classification of Lorentzian holonomy algebras was obtained recently. In the present paper weakly-irreduci…
Holonomy of supermanifoldsmath.DG
Holonomy groups and holonomy algebras for connections on locally free sheaves over supermanifolds are introduced. A one-to-one correspondence between parallel sections and holonomy-invariant vectors, and a one-to-one correspondence between parallel locally direct subsheaves and holonomy-invariant vector supersubspaces …
We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a CR-submanifold of a complex space form. We complete the local classification of normal holonomies for complex submanifolds. We show that the normal holonomy group of a coisotropic submanifold acts as the holonomy representation o…
Proof that Ricci flow preserves full holonomy group.
problem Invariance of full holonomy group under Ricci flow.
method Direct proof using invariance of reduced holonomy.
result Full holonomy group is invariant under Ricci flow.
Researchers create coordinates for hyperbolic surfaces, proving a magic formula.
problem Constructing coordinates for hyperbolic structures on genus-2 surfaces.
method Developed Fenchel-Nielsen coordinates and Wolpert's magic formula analogues.
result Found Darboux charts for the Goldman symplectic form on branched hyperbolic structures.
Holonomy groups of K-contact sub-Riemannian manifolds are studied.
problem Understanding the holonomy groups of K-contact sub-Riemannian manifolds.
method Analyzing the horizontal holonomy group and comparing it to the holonomy group of a Riemannian manifold.
result The horizontal holonomy group either coincides with the holonomy group of a Riemannian manifold or is a codimension-one subgroup.
This article is concerned with the study of the holonomy group of flat solvmanifolds. It is known that the holonomy group of a flat solvmanifold is abelian; we give an elementary proof of this fact and moreover we prove that any finite abelian group is the holonomy group of a flat solvmanifold. Furthermore, we show tha…
This paper classifies holonomy groups of K-contact sub-pseudo-Riemannian manifolds.
problem The problem of subspace degeneracy in indefinite signature metrics.
method Adapted for metrics of indefinite signature, bypassing subspace degeneracy.
result Horizontal holonomy group either coincides with the adapted holonomy group or acts as its normal subgroup of codimension one.
The problem of classification of connected holonomy groups (equivalently of holonomy algebras) for pseudo-Riemannian manifolds is open. The classification of Riemannian holonomy algebras is a classical result. The classification of Lorentzian holonomy algebras was obtained recently. In the present paper weakly-irreduci…
The classification of all possible holonomy algebras of Einstein and vacuum Einstein Lorentzian manifolds is obtained. It is shown that each such algebra appears as the holonomy algebra of an Einstein (resp., vacuum Einstein) Lorentzian manifold, the direct constructions are given. Also the holonomy algebras of totally…
Motivated by Kohno's result on the holonomy Lie algebra of a hyperplane arrangement, we define the holonomy Lie algebra of a finite geometric lattice in a combinatorial way. For a solvable pair of lattices, we show that the holonomy Lie algebra is an almost-direct product of the holonomy Lie algebra of the sublattice a…
The article proves a lower semicontinuity property of holonomy maps.
problem Continuity properties of holonomy maps on manifolds.
method Examined continuity properties of holonomy class and restricted holonomy class maps.
result The restricted holonomy class map is lower semicontinuous.
The aim of this paper is to show that holonomy properties of Finsler manifolds can be very different from those of Riemannian manifolds. We prove that the holonomy group of a positive definite non-Riemannian Finsler manifold of non-zero constant curvature with dimension >2 cannot be a compact Lie group. Hence this holo…
In order to understand the linearization problem around a leaf of a singular foliation, we extend the familiar holonomy map from the case of regular foliations to the case of singular foliations. To this aim we introduce the notion of holonomy transformation. Unlike the regular case, holonomy transformations can not be…
Study holonomy in pseudo-Hermitian geometry structures.
problem Holonomy classification in pseudo-Hermitian geometry.
method Analyzes sub-Riemannian structures, torsion, and holonomy algebras.
result Holonomy groups of Schouten and adapted connections are related under certain conditions.
Our paper is devoted to the study of the holonomy groups of Finsler surfaces using the methods of infinite dimensional Lie theory. The notion of infinitesimal holonomy algebra will be introduced, by the smallest Lie algebra of vector fields on an indicatrix, containing the curvature vector fields and their horizontal c…
We define the equivariant holonomy of an invariant connection on a principal U(1)-bundle. The properties of the ordinary holonomy are generalized to the equivariant setting. In particular, equivariant U(1)-bundles with connection are shown to be classified by its equivariant holonomy modulo isomorphisms. We also show t…
We study the full holonomy group of Lorentzian manifolds with a parallel null line bundle. We prove several results that are based on the classification of the restricted holonomy groups of such manifolds and provide a construction method for manifolds with disconnected holonomy which starts from a Riemannian manifold …
Study on holonomy of Obata connection on Joyce hypercomplex manifolds.
problem Analyzing the holonomy of the Obata connection on Joyce hypercomplex manifolds.
method Examining holonomy groups for different Joyce hypercomplex manifolds.
result Holonomy groups are strictly contained in quaternionic general linear group for most Joyce hypercomplex manifolds.
The paper proves a convergence theorem for Wiener measures on holonomy groups.
problem Understanding convergence of Wiener measures on holonomy groups.
method Using stochastic parallel transports along convergent metric connections.
result Proves a convergence theorem for push-forward Wiener measures on holonomy groups.
Most Finsler metrics have infinite-dimensional holonomy groups.
problem Understanding the holonomy groups of Finsler metrics.
method Analyzing the set of Finsler metrics on a manifold.
result An open dense subset of Finsler metrics have infinite-dimensional holonomy groups.
The classification problem for holonomy of pseudo-Riemannian manifolds is actual and open. In the present paper, holonomy algebras of Lorentz-Kähler manifolds are classified. A simple construction of a metric for each holonomy algebra is given. Complex Walker coordinates are introduced and described using the potential…
The reductive holonomy algebras for a torsion-free affine connection are analysed, with the goal of establishing which ones can correspond to a Ricci-flat connection with the same properties. Various families of holonomies are eliminated through different algebraic means, and examples are constructed (in this paper and…
This paper aims to classify the holonomy of the conformal Tractor connection, and relate these holonomies to the geometry of the underlying manifold. The conformally Einstein case is dealt with through the construction of metric cones, whose Riemmanian holonomy is the same as the Tractor holonomy of the underlying mani…
All candidates to the weakly-irreducible not irreducible holonomy algebras of Lorentzian manifolds are known. In the present paper metrics that realize all these candidates as holonomy algebras are given. This completes the classification of the Lorentzian holonomy algebras. Also new examples of metrics with the holono…
Affine 3-manifolds with centralizing holonomy are complete.
problem Closed flat affine manifolds with parallel volume are not always complete.
method Showed the Markus conjecture holds for 3-manifolds with centralizing holonomy.
result Holonomy centralizing an affine transformation preserves volume completeness.
The study examines geometric properties of complex Hermitian manifolds and their holonomy groups.
problem Understanding the geometric properties and restrictions of Hermitian manifolds and their holonomy groups.
method Analyzing the representation of restricted holonomy groups and their geometric consequences.
result Established criteria for when a Hermitian manifold is Kähler or projective based on its holonomy group.
We classify the holonomy algebras of manifolds admitting an indecomposable torsion free -structure, i.e. for which the holonomy representation does not leave invariant any proper non-degenerate subspace. We realize some of these Lie algebras as holonomy algebras of left-invariant metrics on Lie groups.