We introduce the notions of Chern-Dirac bundles and Chern-Dirac operators on Hermitian manifolds. They are analogues of classical Dirac bundles and Dirac operators, with Levi-Civita connection replaced by Chern connection. We then show that the tensor product of canonical and the anticanonical spinor bundles, called V-…
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48 results for “twisted spinor bundle”
We consider Dirac operators on odd-dimensional compact spin manifolds which are twisted by a product bundle. We show that the space of connections on the twisting bundle which yield an invertible operator has infinitely many connected components if the untwisted Dirac operator is invertible and the dimension of the twi…
Proof that stable minimal surfaces in 3D are flat.
problem Classification of stable minimal surfaces in .
method Index theory for Dirac operators on twisted spinor bundles.
result Every complete two-sided stable minimal surface in is flat.
The study analyzes Dirac operators twisted by specific bundles, revealing their geometric and regularity properties.
problem Analyzing Dirac operators twisted by ramified Euclidean line bundles.
method Describes closed extensions of Dirac operators in terms of Gelfand-Robbin quotient, constructs geometric realizations, and develops an regularity theory.
result Geometric realizations of the Gelfand-Robbin quotient and an regularity theory are constructed.
New rigidity results for warped product domains.
problem Scalar curvature rigidity of domains in warped products.
method Developed a new connection on a twisted spinor bundle and associated Dirac operator.
result Obtained Llarull type scalar curvature rigidity for a general class of domains in a warped product.
Spinors prove rigidity for polyhedral spacetime data.
problem Rigidity of polyhedral spacetime data sets.
method Extending rigidity analysis from spacetime positive mass theorem.
result Dihedral rigidity connects mass theorem, trapped surfaces.
We develop notions of twisted spinor bundle and twisted pre-quantum bundle on quasi-Hamiltonian G-spaces. The main result of this paper is that we construct a Dirac operator with index given by positive energy representation of loop group. This generalizes the quantization of Hamiltonian -spaces to quasi-Hamiltonian…
We derive upper eigenvalue bounds for the Dirac operator of a closed hypersurface in a manifold with Killing spinors such as Euclidean space, spheres or hyperbolic space. The bounds involve the Willmore functional. Relations with the Willmore inequality are briefly discussed. In higher codimension we obtain bounds on t…
Asymptotic Spectral Flowmath.DG
Study the spectral flow of Dirac operators on spinor bundles.
problem Understanding the asymptotic behavior of spectral flow for Dirac operators.
method Variation of eta invariant and local index theory technique.
result Established a uniform estimate of the eta invariant for large parameter values.
It is known that, for Dirac operators on Riemann surfaces twisted by line bundles with Hermitian-Einstein connections, it is possible to obtain estimates for the first eigenvalue in terms of the topology of the twisting bundle \cite{JL2}. Attempts to generalize topological estimates for higher rank bundles or higher di…
The article studies deformations of -harmonic spinors on 3-manifolds.
problem Investigating the local structure of -harmonic spinors on 3-manifolds.
method Uses Nash-Moser Implicit Function Theorem to handle infinite-dimensional obstruction bundle and loss of regularity.
result Near a -harmonic spinor with smooth singular set, the universal moduli space projects to a codimension 1 submanifold.
Results on symplectic spinors and their higher spin versions, concerning representation theory and cohomology properties are presented. Exterior forms with values in the symplectic spinors are decomposed into irreducible modules including finding the hidden symmetry (Schur--Weyl--Howe type duality) given by a represent…
Let G be a compact, semi-simple Lie group and H a maximal rank reductive subgroup. The irreducible representations of G can be constructed as spaces of harmonic spinors with respect to a Dirac operator on the homogeneous space G/H twisted by bundles associated to the irreducible, possibly projective, representations of…
Motivated by the relationship between orthogonal complex structures and spure spinors, we define twisted partially pure spinors in order to characterize spinorially subspaces of Euclidean space endowed with a complex structure.
Study of Dirac operator with chiral boundary conditions on spin manifolds.
problem Reconstructing metrics and connections from boundary data.
method Defining boundary conjugation map and showing its symbolic determination.
result Reconstruction of Riemannian manifolds and spin structures from boundary data.
The paper proves stability for Einstein metrics with special twisted spinors.
problem Stability of Einstein metrics with specific spinor conditions.
method Proves linear semi-stability for a class of Einstein metrics with non-positive scalar curvature.
result Linear semi-stability for Einstein metrics carrying a parallel twisted spin spinor.
We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the special Riemannian holonomy groups just as a classical pure spinor characterizes the special Kähler holonomy. Motivated by certain curvature identities satisfied by manifolds admitting parallel twisted pure spinors, we also…
Revisits zero modes of Dirac operator on Eguchi-Hanson space.
problem Determining zero modes of the Dirac operator on Eguchi-Hanson space.
method Uses spin- spinors and formalism of differential forms to simplify calculations.
result Reproduces known normalisable zero modes of the twisted Eguchi-Hanson Dirac operator.
The paper shows connections can be uniquely determined by their boundary data.
problem Determining unique connections from boundary measurements.
method Defined a Dirichlet-to-Neumann map for twisted Dirac Laplacians and showed its pseudodifferential properties.
result Equal Dirichlet-to-Neumann maps imply locally gauge equivalent connections.
The paper proves geometric rigidity using harmonic twisted spinors and scalar curvature comparison.
problem Proving geometric rigidity for closed Riemannian spin manifolds with specific properties.
method Using Gromov's exact-lift two-form method and harmonic spinors to analyze scalar curvature.
result The original metric is Einstein, and the universal cover is real hyperbolic in the positive-spectrum case.
Study uncoupled solutions to Dirac-Yang-Mills equations on spin manifolds.
problem Condition for vanishing Dirac current on harmonic spinors.
method Perturbation theory and index theorem.
result Existence of uncoupled solutions, classification of connection forms.
In this note we compare the spinor bundle of a Riemannian manifold with the spinor bundles of the Riemannian factors . We show, that - without any holonomy conditions - the spinor bundle of for a special class of metrics is isomorphic to a bundle obtained by tensoring t…
Spinor bundle constructed on loop space for string manifolds.
problem Constructing spinor bundles for string manifolds.
method Using ideas from Stolz and Teichner, a spinor bundle and fusion product are defined for a string manifold.
result Existence of spinor bundle with fusion product on a manifold X if and only if X admits a string structure.
This dissertation explores Clifford bundles and spinor fields in geometric and algebraic contexts.
problem Understanding spinor fields and their classification in geometric frameworks.
method Combines algebraic and geometric approaches to study Clifford structures on bundles and spinor fields.
result Identifies new spinor field classes in warped flux compactifications.
It is known that the bundle of Dirac spinors is produced as a direct sum of two bundles - the bundle of chiral spinors and its Hermitian conjugate bundle. In this paper some aspects of metric connections for chiral and Dirac spinors are resumed and their relation is studied.
Let be an orientable compact flat Riemannian manifold endowed with a spin structure. In this paper we determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles of , and we derive a formula for the corresponding eta series. In the case of manifolds with holonomy group ,…
Study geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.
problem Geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.
method Groupoid approach to pseudodifferential calculus, rescaled bundle.
result Rescaled bundle provides geometric characterization to asymptotic pseudodifferential calculus on spinor bundles.
We study the geometry of type II supergravity compactifications in terms of an oriented vector bundle , endowed with a bundle metric of split signature and further datum. The geometric structure is associated with a so-called generalised -structure and characterised by an -spinor , which we can regard as a …
The paper extends Strichartz's conjecture to spinor bundles over real hyperbolic spaces.
problem Extending Strichartz's conjecture to spinor bundles.
method Characterization of Poisson transform for spinor bundles and uniform estimates.
result Strichartz's conjecture is extended to spinor bundles over real hyperbolic spaces.
Study invariant operators and vanishing theorems in CR geometry.
problem Analyzing invariant operators and vanishing theorems in CR geometry.
method Investigates Kohn-Dirac operators and derives CR invariant twistor operators.
result Proves vanishing theorems for harmonic spinors and Kohn-Rossi groups.
Spinor formalism is the formalism induced by solutions of the Clifford equation (the connecting operators). For the space-time manifold (n = 4), these operators, connecting the tangent and spinor bundle, are operators that are represented by the Dirac matrices in the special basis. Reduced connecting operators are repr…
The paper extends the Hopf differential concept to associative submanifolds in G2-manifolds.
problem Understanding the geometry of associative submanifolds in G2-manifolds.
method Analogy with CMC surfaces in R^3 and use of spinor theory.
result Every non-totally-geodesic associative 3-fold in R^7, T^7, and S^7 admits non-vanishing harmonic twisted spinors.
Supposing that X is a Riemannian manifold, a Z/2 spinor on X is defined by a data set consisting of a closed set in X to be denoted by Z, a real line bundle over X-Z, and a nowhere zero section on X-Z of the tensor product of the real line bundle and a spinor bundle. The set Z and the spinor are jointly constrained by …
Clarifies Einstein-Cartan gravitation with Dirac spinor on generalized frame bundle.
problem Formulating Einstein-Cartan gravitation on a frame bundle.
method Integrates Dirac spinor into the Einstein-Cartan spacetime structure.
result Variational equations imply standard field equations under standard frame bundle condition.
Study quantum diffusion on spectral triples and spinor bundles.
problem Characterize quantum diffusion on almost commutative spectral triples.
method Spin geometry, C *-Dirichlet forms, quantum stochastic flows.
result Existence of covariant quantum stochastic flows on spinor bundles.
The aim of this paper is the construction of spinor bundles of Cartan type over certain non-orientable manifolds.
Constructs a fusion product on spinor bundle over loop space.
problem Describes a fusion product on the spinor bundle over loop space.
method Uses Connes fusion of von Neumann bimodules and string structures.
result Establishes a novel relation between string structures, loop fusion, and Connes fusion of Fock spaces.
Two explicit formulas for metric connections in the bundle of Dirac spinors are studied. Their equivalence is proved. The explicit formula relating the spinor curvature tensor with the Riemann curvature tensor is rederived.
New -instantons found on 3-sphere's spinor bundle.
problem Classifying and constructing -instantons.
method Used -symmetries and asymptotically conical, co-homogeneity one -metric.
result Found new examples of -instantons with obstructed deformations.
Study torsion parallel spinors on Lorentzian 4-manifolds and their evolution flows.
problem Investigate torsion parallel spinors on Lorentzian four-manifolds.
method Geometric study via spinorial polyforms and supersymmetric NS-NS system.
result Globally hyperbolic evolution flow determined by supersymmetric solutions.
I begin by explaining how Riemannian geometry can be understood in terms of principal fibre bundles and connections thereon. I then introduce and motivate the definition of a spinor structure in terms of familiar geometrical ideas. The central result of this thesis is a complete and constructive classification of spino…
Variant of Seiberg-Witten equations for multiple-spinors connects to stability of holomorphic bundles.
problem Detecting stability of holomorphic vector bundles using Seiberg-Witten equations.
method Abelian gauge-theoretic variant of Seiberg-Witten equations for multiple-spinors.
result Constructs a numerical invariant related to stability of holomorphic vector bundles.
We study an energy functional on the universal spinor bundle over a closed -dimensional spin manifold . The critical points of this functional, which is modelled on the total torsion functional of -structures in seven dimensions, are pairs of Ricci-flat metrics and real parallel spinor fields provided that $…
The harmonic sections of the Kaluza-Klein model can be seen as a variant of harmonic maps with additional gauge symmetry. Geometrically, they are realized as sections of a fiber bundle associated to a principal bundle with a connection. In this paper, we investigate geometric and analytic aspects of a model that combin…
New Euclidean supersymmetric solutions found for a specific metric.
problem Constructing Euclidean supersymmetric solutions in minimal gauged supergravity.
method Infinite classes of Euclidean supersymmetric solutions constructed on spindle metrics.
result Found new solutions with distinct holographic renormalized on-shell actions for twist and anti-twist cases.
Operator fields in the bundle of Dirac spinors and their conversion to spatial fields are considered. Some commutator equations are studied with the use of the conversion technique.
We establish, via geometric quantization of the supercotangent bundle sM of (M,g), a correspondence between its conformal geometry and those of the spinor bundle. In particular, the Kosmann Lie derivative of spinors is obtained by quantization of the comoment map, associated to the new Hamiltonian action of conf(M,g) o…
Parallel spinors help characterize G2* structures and isotropic forms.
problem Characterizing G2* structures and isotropic forms on pseudo-Riemannian manifolds.
method Using a correspondence between irreducible parallel spinors and solutions of a differential system for three-forms.
result Explicit description of isotropic irreducible spinors in signature (4,3) and characterization of G2* structures.