Mathematische Annalen, ISSN 0025-5831, 4/2018, Volume 370, Issue 3, pp. 1681 - 1716

We compute the monodromy of the Hitchin fibration for the moduli space of L-twisted $$SL(n,\mathbb {C})$$ SL(n,C) and $$GL(n,\mathbb {C})$$ GL(n,C) -Higgs...

Mathematics, general | Mathematics | 53M12 | 14H60 | 14H70 | 53C07 | LIE-ALGEBRAS | TOPOLOGY | MATHEMATICS | BUNDLES | SYMMETRIC VANISHING LATTICES | MODULI SPACE | SYSTEMS | CURVES | SHEAVES

Mathematics, general | Mathematics | 53M12 | 14H60 | 14H70 | 53C07 | LIE-ALGEBRAS | TOPOLOGY | MATHEMATICS | BUNDLES | SYMMETRIC VANISHING LATTICES | MODULI SPACE | SYSTEMS | CURVES | SHEAVES

Journal Article

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Exotic components of SO(p,q) surface group representations, and their Higgs bundle avatars

Comptes rendus - Mathématique, ISSN 1631-073X, 06/2018, Volume 356, Issue 6, pp. 666 - 673

For semisimple Lie groups, moduli spaces of Higgs bundles on a Riemann surface correspond to representation varieties for the surface fundamental group. In...

MATHEMATICS | SPACES

MATHEMATICS | SPACES

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2018, Volume 370, Issue 4, pp. 2907 - 2953

We consider the moduli space of polystable L-twisted G-Higgs bundles over a compact Riemann surface X, where G is a real reductive Lie group and L is a...

MATHEMATICS | SURFACE GROUP-REPRESENTATIONS

MATHEMATICS | SURFACE GROUP-REPRESENTATIONS

Journal Article

Bulletin of the London Mathematical Society, ISSN 0024-6093, 02/2017, Volume 49, Issue 1, pp. 117 - 132

Motivated by gauge theory under special holonomy, we present techniques to produce holomorphic bundles over certain non‐compact 3‐folds, called building...

53C07 (secondary) | 14D21 | 14F05 (primary) | MATHEMATICS | G-MANIFOLDS | FANO 3-FOLDS | G-INSTANTONS | P4 | MANIFOLDS | TWISTED CONNECTED-SUMS | Mathematics

53C07 (secondary) | 14D21 | 14F05 (primary) | MATHEMATICS | G-MANIFOLDS | FANO 3-FOLDS | G-INSTANTONS | P4 | MANIFOLDS | TWISTED CONNECTED-SUMS | Mathematics

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 11/2016, Volume 106, Issue 11, pp. 1479 - 1497

G 2-Monopoles are solutions to gauge theoretical equations on G 2-manifolds. If the G 2-manifolds under consideration are compact, then any irreducible G...

Geometry | Primary 57R57 | monopole | G 2 -manifold | Theoretical, Mathematical and Computational Physics | Complex Systems | 53C38 | Group Theory and Generalizations | Physics | 53C29 | 53C07

Geometry | Primary 57R57 | monopole | G 2 -manifold | Theoretical, Mathematical and Computational Physics | Complex Systems | 53C38 | Group Theory and Generalizations | Physics | 53C29 | 53C07

Journal Article

manuscripta mathematica, ISSN 0025-2611, 11/2019, Volume 160, Issue 3, pp. 411 - 481

We define functionals generalising the Seiberg–Witten functional on closed $$spin^c$$ s p i n c manifolds, involving higher order derivatives of the curvature...

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 53C23 | 53C21 | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 53C07

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 53C23 | 53C21 | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 53C07

Journal Article

Chinese Annals of Mathematics, Series B, ISSN 0252-9599, 7/2018, Volume 39, Issue 4, pp. 683 - 694

Let M be an n-dimensional differentiable manifold with an affine connection without torsion and T 1 1 (M) its (1, 1)-tensor bundle. In this paper, the authors...

Connections | 53C35 | Tensor bundle | 53C22 | Geodesic | Sasaki metric | Mathematics, general | Semi-symmetry type condition | Mathematics | Applications of Mathematics | 53C07 | MATHEMATICS

Connections | 53C35 | Tensor bundle | 53C22 | Geodesic | Sasaki metric | Mathematics, general | Semi-symmetry type condition | Mathematics | Applications of Mathematics | 53C07 | MATHEMATICS

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 5/2019, Volume 112, Issue 5, pp. 547 - 558

We obtain a vanishing theorem for Yang–Mills–Higgs pairs on Euclidean and hyperbolic spaces in dimensions greater than 4, as well as a regularity theorem more...

Yang–Mills–Higgs pair | 35B45 | Vanishing theorem | 35B65 | Mathematics, general | 35B53 | Mathematics | Regularity | 53C07 | MATHEMATICS | Yang-Mills-Higgs pair

Yang–Mills–Higgs pair | 35B45 | Vanishing theorem | 35B65 | Mathematics, general | 35B53 | Mathematics | Regularity | 53C07 | MATHEMATICS | Yang-Mills-Higgs pair

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 06/2017, Volume 56, Issue 3, p. 1

In this paper, we study semi-stable Higgs sheaves over compact Kahler manifolds. We prove that there is an admissible approximate Hermitian-Einstein structure...

58E15 | 53C07 | KAHLER-MANIFOLDS | EXISTENCE | MATHEMATICS | HERMITIAN-EINSTEIN METRICS | NARASIMHAN | MATHEMATICS, APPLIED | YANG-MILLS CONNECTIONS | RIEMANN SURFACE | THEOREM | HEAT KERNEL | DIMENSIONAL REDUCTION | VECTOR-BUNDLES | Equality

58E15 | 53C07 | KAHLER-MANIFOLDS | EXISTENCE | MATHEMATICS | HERMITIAN-EINSTEIN METRICS | NARASIMHAN | MATHEMATICS, APPLIED | YANG-MILLS CONNECTIONS | RIEMANN SURFACE | THEOREM | HEAT KERNEL | DIMENSIONAL REDUCTION | VECTOR-BUNDLES | Equality

Journal Article

Advances in Mathematics, ISSN 0001-8708, 11/2017, Volume 320, pp. 1009 - 1062

For a real or complex semisimple Lie group and two nested parabolic subgroups , we study parabolic geometries of type . Associated to the group , we introduce...

Bernstein–Gelfand–Gelfand sequence | Invariant differential operator | BGG sequence | Generalized path geometries | Relative BGG resolution | MATHEMATICS | Bernstein-Gelfand-Gelfand sequence | ALGEBRA | PARABOLIC GEOMETRIES | Machinery | Algebra | Magneto-electric machines | Mathematics - Differential Geometry

Bernstein–Gelfand–Gelfand sequence | Invariant differential operator | BGG sequence | Generalized path geometries | Relative BGG resolution | MATHEMATICS | Bernstein-Gelfand-Gelfand sequence | ALGEBRA | PARABOLIC GEOMETRIES | Machinery | Algebra | Magneto-electric machines | Mathematics - Differential Geometry

Journal Article

Annals of Global Analysis and Geometry, ISSN 0232-704X, 6/2019, Volume 55, Issue 4, pp. 623 - 629

In this paper, we prove a Liouville theorem for holomorphic functions on a class of complete Gauduchon manifolds. This generalizes a result of Yau for complete...

Geometry | Mathematical Physics | Gauduchon manifold | Liouville theorem | 58E20 | Analysis | 53C55 | Global Analysis and Analysis on Manifolds | Holomorphic function | Mathematics | Differential Geometry | 53C07 | MATHEMATICS | Manifolds | Theorems | Analytic functions

Geometry | Mathematical Physics | Gauduchon manifold | Liouville theorem | 58E20 | Analysis | 53C55 | Global Analysis and Analysis on Manifolds | Holomorphic function | Mathematics | Differential Geometry | 53C07 | MATHEMATICS | Manifolds | Theorems | Analytic functions

Journal Article

Annals of Global Analysis and Geometry, ISSN 0232-704X, 3/2017, Volume 51, Issue 2, pp. 129 - 154

We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle...

{\mathrm {G}_{2}}$$ G 2 manifold | Theoretical, Mathematical and Computational Physics | 53C55 | Mathematics | Primary 53C07 | 53C25 | 53C29 | Geometry | Metric connection | Vector bundle | Holonomy | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | Secondary 53C22 | Group Theory and Generalizations | Spherically symmetric metric | manifold | MATHEMATICS | TANGENT SPHERE BUNDLES | CHEEGER-GROMOLL-TYPE | NONNEGATIVE CURVATURE | EXCEPTIONAL HOLONOMY | G manifold | POSITIVE RICCI CURVATURE | RIEMANNIAN MANIFOLD | Studies | Algebra | Bundling | Mathematical analysis | Norms | Texts | Vectors (mathematics) | Manifolds (mathematics) | Joints | Symmetry | Mathematics - Differential Geometry

{\mathrm {G}_{2}}$$ G 2 manifold | Theoretical, Mathematical and Computational Physics | 53C55 | Mathematics | Primary 53C07 | 53C25 | 53C29 | Geometry | Metric connection | Vector bundle | Holonomy | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | Secondary 53C22 | Group Theory and Generalizations | Spherically symmetric metric | manifold | MATHEMATICS | TANGENT SPHERE BUNDLES | CHEEGER-GROMOLL-TYPE | NONNEGATIVE CURVATURE | EXCEPTIONAL HOLONOMY | G manifold | POSITIVE RICCI CURVATURE | RIEMANNIAN MANIFOLD | Studies | Algebra | Bundling | Mathematical analysis | Norms | Texts | Vectors (mathematics) | Manifolds (mathematics) | Joints | Symmetry | Mathematics - Differential Geometry

Journal Article

Journal of Geometry, ISSN 0047-2468, 8/2014, Volume 105, Issue 2, pp. 327 - 342

We prove a Theorem on homotheties between two given tangent sphere bundles S r M of a Riemannian manifold M, g of $${{\rm dim}\geq3}$$ dim ≥ 3 , assuming...

Geometry | Primary: 55R25 | Tangent sphere bundle | Secondary: 53A30 | 53C17 | Mathematics | 57R20 | characteristic classes | 53C07 | isometry

Geometry | Primary: 55R25 | Tangent sphere bundle | Secondary: 53A30 | 53C17 | Mathematics | 57R20 | characteristic classes | 53C07 | isometry

Journal Article

Journal of Evolution Equations, ISSN 1424-3199, 6/2018, Volume 18, Issue 2, pp. 549 - 560

In this note, we establish energy identities for vector bundle-valued k-forms satisfying suitable heat-type equations, where the ambient space is equipped with...

58C99 | 53C44 | Harmonic map heat flow | Mathematics | Energy identities | Yang–Mills heat flow | 58J35 | Geometric heat flows | 35K55 | 53C07 | Evolving manifolds | Analysis | Monotonicity

58C99 | 53C44 | Harmonic map heat flow | Mathematics | Energy identities | Yang–Mills heat flow | 58J35 | Geometric heat flows | 35K55 | 53C07 | Evolving manifolds | Analysis | Monotonicity

Journal Article

Communications in Mathematics and Statistics, ISSN 2194-6701, 9/2018, Volume 6, Issue 3, pp. 319 - 358

In this paper, we study the curvature estimate of the Hermitian–Yang–Mills flow on holomorphic vector bundles. In one simple case, we show that the curvature...

58E15 | Mathematics, general | Mathematics | Statistics, general | Hermitian–Yang–Mills flow | Holomorphic structure | Harder–Narasimhan–Seshadri filtration | 53C07

58E15 | Mathematics, general | Mathematics | Statistics, general | Hermitian–Yang–Mills flow | Holomorphic structure | Harder–Narasimhan–Seshadri filtration | 53C07

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 4/2013, Volume 273, Issue 3, pp. 653 - 710

If we consider the moduli space of flat connections of a non trivial principal SO(3)-bundle over a surface, then we can define a map from the set of perturbed...

Adiabatic process | 35J60 | Moduli space | 53C22 | 53D20 | Geodesic | Mathematics, general | Mathematics | Flat connection | Yang–Mills equation | 53C07 | Yang-Mills equation | MATHEMATICS

Adiabatic process | 35J60 | Moduli space | 53C22 | 53D20 | Geodesic | Mathematics, general | Mathematics | Flat connection | Yang–Mills equation | 53C07 | Yang-Mills equation | MATHEMATICS

Journal Article

Journal of Topology, ISSN 1753-8416, 03/2019, Volume 12, Issue 1, pp. 1 - 55

The Seiberg–Witten equation with multiple spinors generalises the classical Seiberg–Witten equation in dimension 3. In contrast to the classical case, the...

57R57 (primary) | 14H60 | 57M27 | 35Q56 | 53C07 | CALIBRATED GEOMETRY | MATHEMATICS | GAUGE-THEORY | BUNDLES | INVARIANTS | 3-MANIFOLDS | MODULI | DIRAC | Mathematics - Differential Geometry

57R57 (primary) | 14H60 | 57M27 | 35Q56 | 53C07 | CALIBRATED GEOMETRY | MATHEMATICS | GAUGE-THEORY | BUNDLES | INVARIANTS | 3-MANIFOLDS | MODULI | DIRAC | Mathematics - Differential Geometry

Journal Article

Communications in Mathematics and Statistics, ISSN 2194-6701, 6/2019, Volume 7, Issue 2, pp. 191 - 206

In this paper, we establish a generalized Hitchin–Kobayashi correspondence between the $$\tau $$ τ -semi-stability and the existence of approximate $$\tau $$ τ...

tau $$ τ -semi-stable | Gauduchon manifolds | 53C55 | Mathematics, general | Holomorphic pair | Mathematics | Statistics, general | Approximate $$\tau $$ τ -Hermitian–Einstein structure | 53C07

tau $$ τ -semi-stable | Gauduchon manifolds | 53C55 | Mathematics, general | Holomorphic pair | Mathematics | Statistics, general | Approximate $$\tau $$ τ -Hermitian–Einstein structure | 53C07

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 2015, Volume 105, Issue 2, pp. 221 - 243

This paper presents a non-self-dual solution of the Yang-Mills equations on a noncommutative version of the classical , so generalizing the classical meron...

17B37 | 53C07 | 81R60 | QUANTUM GROUPS | warped product | CONNECTIONS | PHYSICS, MATHEMATICAL | Yang-Mills equations | Hopf algebras | meron solution | GEOMETRY | Algebra

17B37 | 53C07 | 81R60 | QUANTUM GROUPS | warped product | CONNECTIONS | PHYSICS, MATHEMATICAL | Yang-Mills equations | Hopf algebras | meron solution | GEOMETRY | Algebra

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 2/2015, Volume 174, Issue 1, pp. 25 - 42

We introduce a class of Higgs bundles called cyclic which lie in the Hitchin component of representations of a compact Riemann surface into the split real form...

Geometry | Higgs bundles | Cyclic | 53C43 | Mathematics | Harmonic maps | Toda | 53C07 | MATHEMATICS | SYSTEMS | SURFACES | Mathematics - Differential Geometry

Geometry | Higgs bundles | Cyclic | 53C43 | Mathematics | Harmonic maps | Toda | 53C07 | MATHEMATICS | SYSTEMS | SURFACES | Mathematics - Differential Geometry

Journal Article

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