ACM Transactions on Graphics (TOG), ISSN 0730-0301, 07/2017, Volume 36, Issue 4, pp. 1 - 15

We present a method for locally injective seamless parametrization of triangular mesh surfaces of arbitrary genus, with or without boundaries, given desired...

injective maps | discrete harmonic | global parametrization | mesh parametrization | Mesh parametrization | Global parametrization | Discrete harmonic | Injective maps | COMPUTER SCIENCE, SOFTWARE ENGINEERING | PARAMETERIZATION | MAPPINGS

injective maps | discrete harmonic | global parametrization | mesh parametrization | Mesh parametrization | Global parametrization | Discrete harmonic | Injective maps | COMPUTER SCIENCE, SOFTWARE ENGINEERING | PARAMETERIZATION | MAPPINGS

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 4/2019, Volume 29, Issue 2, pp. 1075 - 1108

The classification problem for holonomy of pseudo-Riemannian manifolds is actual and open. In the present paper, holonomy algebras of Lorentz-Kähler manifolds...

Lorentz-Kähler manifold | Holonomy group | 53C50 | Complex pp-wave | 53C35 | 53C55 | Mathematics | Space of oriented lines | 53C25 | Complex Walker coordinates | 53C29 | Abstract Harmonic Analysis | Fourier Analysis | Symmetric space | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS | Lorentz-Kahler manifold | ALGEBRAS | METRICS | Algebra

Lorentz-Kähler manifold | Holonomy group | 53C50 | Complex pp-wave | 53C35 | 53C55 | Mathematics | Space of oriented lines | 53C25 | Complex Walker coordinates | 53C29 | Abstract Harmonic Analysis | Fourier Analysis | Symmetric space | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS | Lorentz-Kahler manifold | ALGEBRAS | METRICS | Algebra

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 10/2019, Volume 202, Issue 1, pp. 203 - 211

An n-dimensional Bieberbach group is the fundamental group of a closed flat n-dimensional manifold. K. Dekimpe and P. Penninckx conjectured that an...

Bieberbach group | Cyclic group | Crystallographic group | Convex and Discrete Geometry | Algebraic Geometry | Mathematics | Hyperbolic Geometry | Generators | Projective Geometry | Topology | Differential Geometry | MATHEMATICS | NUMBER

Bieberbach group | Cyclic group | Crystallographic group | Convex and Discrete Geometry | Algebraic Geometry | Mathematics | Hyperbolic Geometry | Generators | Projective Geometry | Topology | Differential Geometry | MATHEMATICS | NUMBER

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 1/2019, Volume 29, Issue 1, pp. 33 - 82

We prove that the Cauchy problem for parallel null vector fields on smooth Lorentzian manifolds is well-posed. The proof is based on the derivation and...

83C05 | Parallel spinors | Symmetric hyperbolic system | Primary 53C50 | 53C44 | 53C27 | Mathematics | 35L02 | 35L10 | Cauchy problem | 53C29 | Abstract Harmonic Analysis | Lorentzian geometry | Secondary 53C26 | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Killing spinors | Differential Geometry | Dynamical Systems and Ergodic Theory | Holonomy groups | Parallel null vector field | MATHEMATICS | CAUCHY-PROBLEMS | METRICS | MANIFOLDS

83C05 | Parallel spinors | Symmetric hyperbolic system | Primary 53C50 | 53C44 | 53C27 | Mathematics | 35L02 | 35L10 | Cauchy problem | 53C29 | Abstract Harmonic Analysis | Lorentzian geometry | Secondary 53C26 | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Killing spinors | Differential Geometry | Dynamical Systems and Ergodic Theory | Holonomy groups | Parallel null vector field | MATHEMATICS | CAUCHY-PROBLEMS | METRICS | MANIFOLDS

Journal Article

Quarterly Journal of Mathematics, ISSN 0033-5606, 12/2016, Volume 67, Issue 4, pp. 743 - 755

Let G be a connected complex Lie group or a connected amenable Lie group. We show that any flat principal G-bundle over any finite CW-complex pulls back to a...

MATHEMATICS | DISCRETE STRUCTURE GROUP | VECTOR BUNDLES | SOLVABLE HOLONOMY | Mathematics

MATHEMATICS | DISCRETE STRUCTURE GROUP | VECTOR BUNDLES | SOLVABLE HOLONOMY | Mathematics

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 1/2015, Volume 25, Issue 1, pp. 281 - 297

An SU(3)- or SU(1,2)-structure on a 6-dimensional manifold N 6 can be defined as a pair of a 2-form ω and a 3-form ρ. We prove that any analytic SU(3)- or...

Exceptional holonomy | 53C44 | 53C10 | Mathematics | Stable forms | 53C29 | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Hitchin’s flow equation | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS | SPIN | METRICS | MANIFOLDS | Hitchin's flow equation | SU/U | Resveratrol

Exceptional holonomy | 53C44 | 53C10 | Mathematics | Stable forms | 53C29 | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Hitchin’s flow equation | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS | SPIN | METRICS | MANIFOLDS | Hitchin's flow equation | SU/U | Resveratrol

Journal Article

ACM Transactions on Graphics, ISSN 0730-0301, 08/2008, Volume 27, Issue 3, p. 1

We present a discrete treatment of adapted framed curves, parallel transport, and holonomy, thus establishing the language for a discrete geometric model of...

Rods | Discrete differential geometry | Strands | Discrete holonomy | COMPUTER SCIENCE, SOFTWARE ENGINEERING | NUMBER | INSTABILITY | DYNAMICS | rods | discrete differential geometry | discrete holonomy | SIMULATION | strands

Rods | Discrete differential geometry | Strands | Discrete holonomy | COMPUTER SCIENCE, SOFTWARE ENGINEERING | NUMBER | INSTABILITY | DYNAMICS | rods | discrete differential geometry | discrete holonomy | SIMULATION | strands

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 12/2018, Volume 28, Issue 4, pp. 3139 - 3170

In this paper, a metric with $$\hbox {G}_2$$ G 2 holonomy and slow rate of convergence to the cone metric is constructed on a ball inside the cone over the...

Abstract Harmonic Analysis | Special holonomy | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Ricci-flat | Mathematics | 53C25 | Differential Geometry | Dynamical Systems and Ergodic Theory | G_2 holonomy | 53C29

Abstract Harmonic Analysis | Special holonomy | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Ricci-flat | Mathematics | 53C25 | Differential Geometry | Dynamical Systems and Ergodic Theory | G_2 holonomy | 53C29

Journal Article

JOURNAL OF HIGH ENERGY PHYSICS, ISSN 1029-8479, 03/2018, Issue 3

We revisit our construction of mirror symmetries for compactifications of Type II superstrings on twisted connected sum G(2) manifolds. For a given G(2)...

SUPERSYMMETRY | FANO 3-FOLDS | FIELD-THEORIES | SINGULARITIES | String Duality | DISCRETE TORSION | 3 DIMENSIONS | Supersymmetry and Duality | EXCEPTIONAL HOLONOMY MANIFOLDS | SUBMANIFOLDS | THEORY COMPACTIFICATIONS | SURFACES | PHYSICS, PARTICLES & FIELDS

SUPERSYMMETRY | FANO 3-FOLDS | FIELD-THEORIES | SINGULARITIES | String Duality | DISCRETE TORSION | 3 DIMENSIONS | Supersymmetry and Duality | EXCEPTIONAL HOLONOMY MANIFOLDS | SUBMANIFOLDS | THEORY COMPACTIFICATIONS | SURFACES | PHYSICS, PARTICLES & FIELDS

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 1998, Volume 524, Issue 1, pp. 269 - 282

We consider Type II string theories on T-n/Z(2)(m) Joyce orbifolds. This class contains orbifolds which can be desingularised to give manifolds of G(2) (n = 7)...

DUALITY | ORBIFOLDS | COMPACT RIEMANNIAN 7-MANIFOLDS | DISCRETE TORSION | D-BRANES | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

DUALITY | ORBIFOLDS | COMPACT RIEMANNIAN 7-MANIFOLDS | DISCRETE TORSION | D-BRANES | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

Journal of the Korean Mathematical Society, ISSN 0304-9914, 2007, Volume 44, Issue 3, pp. 615 - 626

A pair of pants Sigma (0, 3) is a building block of oriented surfaces. The purpose of this paper is to determine the discrete conditions for the holonomy group...

A pair of pants | Hyperbolic structure | Hyperbolic matrix | Discrete holonomy group | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | a pair of pants | hyperbolic matrix | hyperbolic structure | discrete holonomy group

A pair of pants | Hyperbolic structure | Hyperbolic matrix | Discrete holonomy group | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | a pair of pants | hyperbolic matrix | hyperbolic structure | discrete holonomy group

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 1999, Volume 100, Issue 1, pp. 1 - 57

TRACE CLASS CONJECTURE | LIMIT FORMULAS | MATHEMATICS | DISCRETE-SERIES | REPRESENTATIONS | SYMMETRIC-SPACES | MANIFOLDS | SPECTRUM | RAMANUJAN DUALS | HOMOLOGY | MULTIPLICITIES | 11F72 | 11M36 | 37C35 | 22E45

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 6/2019, Volume 200, Issue 1, pp. 93 - 103

We prove that the holonomy map from the set of equivalence classes of parabolic complex projective structures on compact surfaces with finitely many punctures...

Holonomy map | 37F75 | 34M35 | Mathematics | 34M45 | Topology | Foliations | Convex and Discrete Geometry | Algebraic Geometry | Complex projective structures | Hyperbolic Geometry | Projective Geometry | Differential Geometry

Holonomy map | 37F75 | 34M35 | Mathematics | 34M45 | Topology | Foliations | Convex and Discrete Geometry | Algebraic Geometry | Complex projective structures | Hyperbolic Geometry | Projective Geometry | Differential Geometry

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 10/2015, Volume 25, Issue 4, pp. 2687 - 2697

In this paper, we study the uniqueness in the de Rham–Wu decomposition for pseudo-Riemannian manifolds.

Holonomy group | 53B30 | 53C50 | De Rham decomposition | Mathematics | 53C29 | Abstract Harmonic Analysis | Lorentzian manifold | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Pseudo-Riemannian manifold | Differential Geometry | Dynamical Systems and Ergodic Theory | HOLONOMY GROUPS | MATHEMATICS | METRICS | CLASSIFICATION | MANIFOLDS | De Rham decomposition

Holonomy group | 53B30 | 53C50 | De Rham decomposition | Mathematics | 53C29 | Abstract Harmonic Analysis | Lorentzian manifold | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Pseudo-Riemannian manifold | Differential Geometry | Dynamical Systems and Ergodic Theory | HOLONOMY GROUPS | MATHEMATICS | METRICS | CLASSIFICATION | MANIFOLDS | De Rham decomposition

Journal Article

Journal of the Korean Mathematical Society, ISSN 0304-9914, 2014, Volume 51, Issue 2, pp. 403 - 426

The purpose of this paper is to find expressions of the Fricke spaces of some basic surfaces which are a three-holed sphere Sigma(0, 3), a one-holed torus...

Discrete holonomy group | Involution | Fricke space | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | involution | discrete holonomy group

Discrete holonomy group | Involution | Fricke space | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | involution | discrete holonomy group

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 7/2019, Volume 29, Issue 3, pp. 2147 - 2216

In this article, we study the deformation theory of conically singular Cayley submanifolds. In particular, we prove a result on the expected dimension of a...

Abstract Harmonic Analysis | Special holonomy | Fourier Analysis | Convex and Discrete Geometry | Calibrated geometry | Global Analysis and Analysis on Manifolds | 53C38 | Mathematics | Differential Geometry | Dynamical Systems and Ergodic Theory | Conical singularities | MATHEMATICS | ASSOCIATIVE SUBMANIFOLDS | SPECIAL LAGRANGIAN SUBMANIFOLDS

Abstract Harmonic Analysis | Special holonomy | Fourier Analysis | Convex and Discrete Geometry | Calibrated geometry | Global Analysis and Analysis on Manifolds | 53C38 | Mathematics | Differential Geometry | Dynamical Systems and Ergodic Theory | Conical singularities | MATHEMATICS | ASSOCIATIVE SUBMANIFOLDS | SPECIAL LAGRANGIAN SUBMANIFOLDS

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2012, Volume 255, Issue 1, pp. 1 - 23

In the spirit of the Goodman-Plante average condition for the existence of a transverse invariant measure for foliations, we give an averaging condition to...

Lamination | Discrete equivalence relation | Measure | MATHEMATICS | lamination | measure | FOLIATIONS | HOLONOMY | DYNAMICS | MANIFOLDS | discrete equivalence relation | Mathematics

Lamination | Discrete equivalence relation | Measure | MATHEMATICS | lamination | measure | FOLIATIONS | HOLONOMY | DYNAMICS | MANIFOLDS | discrete equivalence relation | Mathematics

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 7/2018, Volume 28, Issue 3, pp. 2206 - 2224

We prove that, under reasonable conditions, odd co-dimension Riemannian foliations cannot occur in positively curved manifolds.

53C20 | Positive sectional curvature | 53C12 | 57R30 | Mathematics | Abstract Harmonic Analysis | Fourier Analysis | Holonomy | Convex and Discrete Geometry | Riemannian foliations | Global Analysis and Analysis on Manifolds | Wilhelm conjecture | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS | NONNEGATIVE SECTIONAL CURVATURE | SUBMERSIONS

53C20 | Positive sectional curvature | 53C12 | 57R30 | Mathematics | Abstract Harmonic Analysis | Fourier Analysis | Holonomy | Convex and Discrete Geometry | Riemannian foliations | Global Analysis and Analysis on Manifolds | Wilhelm conjecture | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS | NONNEGATIVE SECTIONAL CURVATURE | SUBMERSIONS

Journal Article

Geometry and Topology, ISSN 1465-3060, 08/2017, Volume 21, Issue 5, pp. 3047 - 3092

We answer affirmatively a question posed by Morita on homological stability of surface diffeomorphisms made discrete. In particular, we prove that...

MATHEMATICS | BUNDLES | FOLIATIONS | STABILITY | HOLONOMY | MORITA-MUMFORD CLASSES | MANIFOLDS | MAPPING CLASS GROUP | HOMOTOPY | MODULI SPACES

MATHEMATICS | BUNDLES | FOLIATIONS | STABILITY | HOLONOMY | MORITA-MUMFORD CLASSES | MANIFOLDS | MAPPING CLASS GROUP | HOMOTOPY | MODULI SPACES

Journal Article

International Journal of Theoretical Physics, ISSN 0020-7748, 7/2018, Volume 57, Issue 7, pp. 2093 - 2102

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the...

Yang-Mills theory | Theoretical, Mathematical and Computational Physics | Gauge invariance | Quantum Physics | Physics, general | Physics | Elementary Particles, Quantum Field Theory | Discretized model | Business administration | Pattern Formation and Solitons | Mathematical Physics | Analysis of PDEs | Library and information sciences | Operator Algebras | Mathematics | Nonlinear Sciences | Humanities and Social Sciences | General Mathematics | Chaotic Dynamics | Spectral Theory | Differential Geometry | Metric Geometry | Exactly Solvable and Integrable Systems

Yang-Mills theory | Theoretical, Mathematical and Computational Physics | Gauge invariance | Quantum Physics | Physics, general | Physics | Elementary Particles, Quantum Field Theory | Discretized model | Business administration | Pattern Formation and Solitons | Mathematical Physics | Analysis of PDEs | Library and information sciences | Operator Algebras | Mathematics | Nonlinear Sciences | Humanities and Social Sciences | General Mathematics | Chaotic Dynamics | Spectral Theory | Differential Geometry | Metric Geometry | Exactly Solvable and Integrable Systems

Journal Article

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