The Carrollian superplane is constructed as a supermanifold generalization of the Carrollian plane.
problem Constructing the Carrollian superplane as a supermanifold.
method Intrinsic construction of the Carrollian superplane as a supermanifold generalization of the Carrollian plane, defining Carroll spinors, and showing it as a principal R1∣2-bundle. result Novel N=2 Carrollian supersymmetry transformations are generated. Weyl-type theorems extended to Galilei and Carroll geometries.
problem Extending Weyl's theorem to non-relativistic and ultra-relativistic spacetimes.
method Defining and analyzing conformal and projective structures in Galilei and Carroll geometries.
result Torsion-free connections in Galilei and Carroll geometries are uniquely determined by their projective structures.
Study of potential Carroll structures and special Carrollian manifolds for null hypersurfaces.
problem Understanding intrinsic geometry of null hypersurfaces.
method Initiate study of potential Carroll structures and explore their relationship to special Carrollian manifolds.
result Initiate the study of potential Carroll structures and their relationship to special Carrollian manifolds.
Introduces Carrollian Lie algebroids to handle singular Carrollian geometries.
problem Handling singular Carrollian geometries within standard Carrollian geometry.
method Introduces Carrollian Lie algebroids to study singular Carrollian geometries.
result Established the existence of compatible connections on Carrollian Lie algebroids.
New tractor geometry derived from asymptotically flat spacetimes.
problem Understanding the geometry of spacetimes near their boundaries.
method Derived null-tractor bundle from interior spacetime geometry, proved connections' uniqueness, and expressed results in BMS coordinates.
result Tractor connection encodes mass and angular momentum in 3D, and asymptotic shear in higher dimensions.
The paper classifies intrinsic torsion in various spacetime structures.
problem Classifying intrinsic torsion in different spacetime structures.
method Review and classification of intrinsic torsion in galilean, Carrollian, Aristotelian, and Bargmannian spacetime structures.
result Found 16 classes for Aristotelian structures and 27 for Bargmannian structures.
Gauging procedure constructs lagrangians for carrollian gravity.
problem Constructing lagrangians for carrollian gravity.
method Gauging procedure applied to Klein pairs corresponding to homogeneous spaces.
result Generalizes first-order lagrangians for four-dimensional maximally symmetric carrollian spaces.
New spinor types found on certain manifolds.
problem Understanding spinor structures on manifolds.
method Introducing and proving existence of Ricci Killing spinors.
result New examples of manifolds with generalized Killing spinors.
Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.
Symmetry operators of twistor spinors and harmonic spinors can be constructed from conformal Killing-Yano forms. Transformation operators relating twistors to harmonic spinors are found in terms of potential forms. These constructions are generalized to gauged twistor spinors and gauged harmonic spinors. The operators …
Explains non-lorentzian theories and their dynamics.
problem Understanding non-lorentzian kinematics and dynamics.
method Review of kinematical spacetimes, construction of particle dynamics actions, discussion of gravity theories and field theories.
result Introduction and analysis of non-lorentzian gravity and field theories.
We study generalized Killing spinors on round spheres Sn. We show that on the standard sphere S8 any generalized Killing spinor has to be an ordinary Killing spinor. Moreover we classify generalized Killing spinors on Sn whose associated symmetric endomorphism has at most two eigenva…
We provide explicit spinor representations for Clifford algebras.
problem Building explicit representations of Clifford algebras.
method Explicit construction of spinor modules and parallel spinor fields.
result Explicit spinor representations for all mixed signature Clifford algebras.
We consider gauged twistor spinors which are supersymmetry generators of supersymmetric and superconformal field theories in curved backgrounds. We show that the spinor bilinears of gauged twistor spinors satify the gauged conformal Killing-Yano equation. We prove that the symmetry operators of the gauged twistor spino…
This paper studies Sasakian quasi-Killing spinors on 3D Sasakian manifolds.
problem Characterizing Sasakian quasi-Killing spinors on 3D Sasakian manifolds.
method Detailed analysis and geometric properties of Sasakian quasi-Killing spinors.
result Almost all Sasakian quasi-Killing spinors solve the Einstein-Dirac system with a non-zero cosmological constant.
Study on hypersurfaces in Einstein manifolds using Killing spinors.
problem Characterizing hypersurfaces in Einstein manifolds.
method Describes PDEs for induced spinors and proves embedding results.
result Embedding results for real analytic pseudo-Riemannian manifolds.
In this review, basic definitions of spin geometry are given and some of its applications to supersymmetry, supergravity and condensed matter physics are summarized. Clifford algebras and spinors are defined and the first-order differential operators on spinors which lead to the definitions of twistor and Killing spino…
New method classifies spinor orbits in dimensions up to 14.
problem Classify orbits of the spin group in semi-spinor spaces.
method Use pure spinors and combinatorial constraints to classify orbits.
result Classification of spinor orbits in dimensions up to 14.
Investigates parallel spinors on Eguchi-Hanson metrics.
problem Analyzing parallel spinors on specific metrics.
method Investigated parallel spinors on Eguchi-Hanson metrics with harmonic spinors.
result Found complex 2-dimensional space of complex parallel spinors and solutions for metrics with zero scalar curvature.
New spinorial field equation reveals geometric properties of Sasaki manifolds.
problem Exploring new spinorial field equations on Sasaki manifolds.
method Developed H-Killing spinors for 3-(α,δ)-Sasaki manifolds. result Obtained one-to-one correspondence between H-Killing spinors on dual pairs of Sasaki spaces. Generalization of twistor spinors to Kähler manifolds which are called Kählerian twistor spinors are considered. We find the differential equation satisfied by the bilinear forms of Kählerian twistor spinors. We show that the bilinear form equation reduces to Kählerian conformal Killing-Yano equation under special cond…
Study of higher spin Killing spinors on 3D manifolds, proving rigidity and providing explicit expressions.
problem Understanding higher spin Killing spinors on 3D manifolds.
method Definition and detailed study of higher spin Killing spinors in arbitrary dimension, focusing on 3D manifolds. Rigidity result and explicit expressions for 3-sphere and 3-hyperbolic space.
result Proved a rigidity result for 3D manifolds admitting higher spin Killing spinors and provided explicit expressions for these spinors.
In this paper, we extend the study of generalized Killing spinors on Riemannian Spinc manifolds started by Moroianu and Herzlich to complex Killing functions. We prove that such spinor fields are always real Spinc Killing spinors or imaginary generalized Spinc Killing spinors, providing that the dimension of t…
Paper studies flows of spinor fields with flux for unified theories.
problem Existence of covariantly constant spinors in unified theories.
method Introduces parabolic flows of spinor fields to find stationary points.
result Establishes short-time existence and smoothing estimates for spinor flows.
The basic first-order differential operators of spin geometry that are Dirac operator and twistor operator are considered. Special types of spinors defined from these operators such as twistor spinors and Killing spinors are discussed. Symmetry operators of massless and massive Dirac equations are introduced and releva…
Classifies invariant generalised Killing spinors on Lie groups.
problem Classifying invariant generalised Killing spinors on Lie groups.
method Complete classification using invariant properties and computational methods.
result Existence of non-trivial invariant generalised Killing spinors implies all invariant spinors are generalised Killing with the same endomorphism.
Extends spinor-horosphere correspondence to higher dimensions and new spinor types.
problem Constructing isomorphisms between spinors and horospheres in hyperbolic spaces.
method Generalizes Mathews' results to Lipschitz spinors and null multiflags in higher-dimensional hyperbolic spaces.
result Equivariant correspondence between two-component Lipschitz spinors and higher-dimensional horospheres.
Study infinitesimal deformations of Killing spinors on nearly parallel G2-manifolds.
problem Infinitesimal deformations of Killing spinors on nearly parallel G2-manifolds.
method Examined using the correspondence between nearly parallel G2-structures and Killing spinors.
result Identified that the space of Rarita-Schwinger fields coincides with a subspace of the eigenspace of the Laplacian.
In this paper, we study the existence of a skew Killing spinor (see the definition below) on 2 and 3-dimensional Riemannian spin manifolds. We establish the integrability conditions and prove that these spinor fields correspond to twistor spinors in the two dimensional case while, up to a conformal change of the metric…
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.
On a Kähler spin manifold Kählerian twistor spinors are a natural analogue of twistor spinors on Riemannian spin manifolds. They are defined as sections in the kernel of a first order differential operator adapted to the Kähler structure, called Kählerian twistor (Penrose) operator. We study Kählerian twistor spinors a…
This paper classifies 4D spin manifolds with skew Killing spinors.
problem Classifying 4D Riemannian spin manifolds with skew Killing spinors.
method Analyzing skew Killing spinors with skew-symmetric endomorphisms A, considering both degenerate and non-degenerate cases.
result In the degenerate case, the manifold is locally isometric to R x N with N having a skew Killing spinor.
We consider some natural infinitesimal Einstein deformations on Sasakian and 3-Sasakian manifolds. Some of these are infinitesimal deformations of Killing spinors and further some integrate to actual Killing spinor deformations. In particular, on 3-Sasakian 7 manifolds these yield infinitesimal Einstein deformations pr…
Calculates spinor heat flow using Gaussian-Grassmann integrals.
problem Computing the spinor heat flow symbol.
method Getzler calculus and Gaussian-Grassmann integrals.
result Computed the spinor heat flow symbol.
Classifies manifolds with specific spinors and constructs parallel spinors.
problem Classifying manifolds with generalized Killing spinors.
method Explicitly constructs parallel spinors and considers modified Dirac currents.
result Classifies Riemannian spin^c manifolds with type I and II imaginary generalized Killing spinors.
The paper studies parallel spinor flows on 3D Cauchy hypersurfaces and provides initial data characterizations.
problem Characterizing parallel spinors on Ricci flat Lorentzian four-manifolds.
method Evolution flow defined by parallel spinors, proving preservation of constraints, solving left-invariant flows.
result Initial data characterization of parallel spinors on Ricci flat Lorentzian four-manifolds.
Characterizes invariant spinors on flag manifolds.
problem Existence of non-trivial invariant spinors on flag manifolds.
method Based on combinatorial properties of positive roots.
result Bounds for the dimension of invariant 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 …
In this paper, we study spinor Bishop equations of curves in E^3. We research the spinor formulations of curves according to Bishop frames in E^3. Also, the relation between spinor formulations of Bishop frames and Frenet frame are expressed.
In this note we compare the spinor bundle of a Riemannian manifold (M=M1×...×MN,g) with the spinor bundles of the Riemannian factors (Mi,gi). We show, that - without any holonomy conditions - the spinor bundle of (M,g) for a special class of metrics is isomorphic to a bundle obtained by tensoring t…
Study finds holonomy algebras for Lorentzian Weyl spin manifolds with specific spinors.
problem Characterizing Lorentzian Weyl spin manifolds with weighted parallel spinors.
method Analyzing holonomy algebras and introducing special coordinates.
result Local forms and examples of Lorentzian Weyl spin manifolds with weighted parallel spinors.
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.
Study on harmonic spinors on specific Lie groups.
problem Existence of left-invariant harmonic spinors on 3D Lie groups.
method Revised spin Dirac operator formula for left-invariant spinors, identified constraints on Lie algebras, and classified metrics with harmonic spinors.
result Identified conditions and metrics for left-invariant harmonic spinors on 3D Lie groups.
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…
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.
Characterizes algebraic squares of irreducible complex spinors in various dimensions.
problem Understanding the relationship between spinors and exterior forms in different dimensions.
method Formalism using geometric product and algebraic relations.
result General correspondence between irreducible complex spinors and algebraically constrained exterior forms.
Study pp-waves with lightlike parallel spinors in vacuum spacetimes.
problem Characterize pp-waves with lightlike parallel spinors in vacuum spacetimes.
method Parametrize pp-wave spacetimes, show correspondence with Riemannian metrics, prove parallel spinor condition.
result A pp-wave spacetime with a lightlike parallel spinor corresponds to a Ricci-flat metric with a parallel spinor.
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.