Killing-Yano and conformal Killing-Yano superalgebras are rigid in constant curvature manifolds.
problem Understanding the rigidity of Killing-Yano and conformal Killing-Yano superalgebras in constant curvature manifolds.
method Defining Z-gradations and filtrations, showing trivial second cohomology groups, and proving non-deformability. result Killing-Yano and conformal Killing-Yano superalgebras are rigid and correspond to geometric invariants of constant curvature manifolds.
We show that the first-order symmetry operators of twistor spinors can be constructed from conformal Killing-Yano forms in conformally-flat backgrounds. We express the conditions on conformal Killing-Yano forms to obtain mutually commuting symmetry operators of twistor spinors. Conformal superalgebras which consist of …
Extends symmetry superalgebras to include all hidden symmetries of manifolds.
problem Tackles hidden symmetries of manifolds generated by Killing spinors.
method Defines generalized symmetry superalgebras, constructs Lie algebra structure, and defines symmetry operators.
result Constructs special Killing-Yano and conformal Killing-Yano forms from bilinears of Killing spinors.
Extended superalgebras from twistor and Killing spinors in constant curvature and Einstein manifolds.
problem Constructing extended superalgebras from twistor and Killing spinors.
method Using twistor and Killing spinors, symmetry operators, and KY/CKY forms, extended superalgebras are constructed.
result Extended Killing and conformal superalgebras are constructed in constant curvature and Einstein manifolds.
The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is…
We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing-Yano forms. A new Lie bracket for conformal Killing-Yano forms that corresponds to slightly modified Schouten-Nijenhuis bracket of differential forms is proposed. We show that conformal Killing-Yano forms satisfy a gr…
Study Minkowski formula for conformal Killing-Yano 2-forms in constant curvature spacetimes.
problem Derive Minkowski formula for conformal Killing-Yano 2-forms.
method Analyze spacetime Alexandrov theorem with a free boundary.
result Established spacetime Alexandrov theorem with a free boundary.
We show that the Euclidean Kerr-NUT-(A)dS metric in 2m dimensions locally admits 2m hermitian complex structures. These are derived from the existence of a non-degenerate closed conformal Killing-Yano tensor with distinct eigenvalues. More generally, a conformal Killing-Yano tensor, provided its exterior derivativ…
We show the existence of conformal Killing-Yano tensors on a manifold endowed with a mixed 3-Sasakian structure.
Harmonic spinors linked to twistor spinors via potential forms and conformal Killing-Yano forms.
problem Connecting harmonic spinors and twistor spinors using mathematical operators.
method Constructing symmetry operators from conformal Killing-Yano forms and finding transformation operators between twistor and harmonic spinors in terms of potential forms.
result Operators transforming gauged twistor spinors to gauged harmonic spinors and algebraic conditions for Seiberg-Witten equations solutions.
Researchers derive symmetry operators from twistor spinors in curved spacetime.
problem Deriving symmetry operators for gauged twistor spinors in curved backgrounds.
method Using gauged twistor spinors and conformal Killing-Yano forms, symmetry operators are constructed.
result Symmetry operators can be obtained from ordinary twistor spinors in constant curvature backgrounds.
The integrability conditions for the existence of Killing-Yano tensors or, equivalently, covariantly closed conformal Killing-Yano tensors, in the presence of torsion are worked out. As an application, all metrics and torsions compatible with the existence of a Killing-Yano tensor of order n-1 are obtained. Finally, th…
Study BGG operators on homogeneous conformal geometries.
problem Finding solutions to BGG operators on homogeneous conformal geometries.
method Invariant calculus for algebraic computations.
result Explicit solutions found for conformal Killing tensors, forms, and spinors.
Estimates quasi-local mass using Minkowski formula and conformal Killing-Yano forms.
problem Estimating quasi-local mass in various spacetimes.
method Applying Minkowski formula to conformal Killing-Yano forms in different spacetimes.
result Obtains rigidity theorems characterizing spacetimes.
The properties of a Killing-Yano tensor of order n-1 in an n-dimensional manifold are investigated. The integrability conditions are worked out and all metrics admitting a Killing-Yano tensor of order n-1 are found. It is pointed out a connection between such tensors and a generalization of the concept of angular momen…
Spin geometry reviewed with applications in physics.
problem None explicitly stated, but related to spin geometry and its applications.
method Definitions of spin geometry, Clifford algebras, and spinors; discussion of differential operators, twistor and Killing spinors; holonomy classification; construction of symmetry operators and extended superalgebras.
result Construction of extended superalgebras and methods to find solutions of Seiberg-Witten equations.
We use the manifestly conformally invariant description of a Lorentzian conformal structure in terms of a parabolic Cartan geometry in order to introduce a superalgebra structure on the space of twistor spinors and normal conformal vector fields formulated in purely algebraic terms on parallel sections in tractor bundl…
The study generalizes twistor spinors to Kähler manifolds and finds bilinear form equations.
problem Generalizing twistor spinors to Kähler manifolds.
method Finding differential equations and reducing them to conformal Killing-Yano equations.
result Bilinear forms of Kählerian twistor spinors reduce to Kählerian conformal Killing-Yano equations under certain conditions.
Researchers describe a method to construct Ricci-flat metrics on a specific surface.
problem Constructing Ricci-flat metrics on a del Pezzo surface.
method Developed a framework and explicitly constructed the first-order deformation of the orthotoric metric.
result The deformation of the conformal Killing-Yano form does not exist.
The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY) tensor as a ``hidden'' symmetry which provides the separation of variables for the geodesic…
Study invariant CKY 2-forms on 5D Lie groups, classifying and determining their properties.
problem Classifying and understanding CKY 2-forms on 5D Lie groups.
method Classification and analysis of 5D metric Lie algebras with CKY tensors.
result First examples of CKY 2-forms on metric Lie algebras without Sasakian structures.
Study finds all hyper-Kähler 4-manifolds with specific symmetries and structures.
problem Characterizing hyper-Kähler 4-manifolds with conformal Kähler structures.
method Analyzing twistor elementary states and locally flat spaces, showing compatibility and incompatibility of complex structures.
result Only hyper-Kähler 4-metric with a non-constant Killing-Yano tensor is the half-flat Taub-NUT instanton.
The paper develops a comprehensive theory of submanifolds in conformal geometries.
problem Understanding submanifolds in conformal geometries of arbitrary dimension.
method Using conformal tractor calculus, the paper provides a new framework for studying submanifolds.
result The theory includes a new notion of distinguished submanifolds and characterizes them in various dimensions.
Study finds only complex 2-step nilpotent Lie groups have Killing-Yano forms.
problem Characterizing Lie groups with Killing-Yano forms.
method Analyzing 2-step nilpotent Lie groups and connected graphs.
result Only complex 2-step nilpotent Lie groups have non-degenerate Killing-Yano forms.
New currents derived from Killing-Yano tensors for gravity.
problem Finding new conserved currents in gravity.
method Using relations involving Riemann, Ricci, and Einstein tensors to introduce novel conserved currents.
result New currents derived from Killing-Yano tensors and their implications for conserved charges.
We classify all spacetimes with a closed rank-2 conformal Killing-Yano tensor. They give a generalization of Kerr-NUT-de Sitter spacetimes. The Einstein condition is explicitly solved and written as an indefinite integral. It is characterized by a polynomial in the integrand. We briefly discuss the smoothness condition…
Novel Lie-superalgebraic description of superstring dynamics.
problem Describing superstring dynamics in super-Minkowskian background.
method Cartan-Eilenberg super-1-gerbe geometrising higher gauge field.
result Manifestly supersymmetric model of supermanifolds.
Study finds necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.
problem Understanding the asymptotic behavior of black hole geometries.
method Used hidden symmetry and conformal geometry technology to find necessary conditions.
result Necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.
Study of n-ary differential operators on weighted densities with canonical symbol and quantization maps.
problem Analysis of n-ary differential operators acting on weighted densities. method Existence and uniqueness of conformally equivariant symbol maps and quantization maps.
result Existence and explicit expression of conformally equivariant symbol and quantization maps.
In this paper, we consider the symmetries of the Dirac operator derived from a connection with skew-symmetric torsion. We find that the generalized conformal Killing-Yano tensors give rise to symmetry operators of the massless Dirac equation, provided an explicitly given anomaly vanishes. We show that this gives rise t…
We consider bosonic supersymmetric backgrounds of ten-dimensional conformal supergravity. Up to local conformal isometry, we classify the maximally supersymmetric backgrounds, determine their conformal symmetry superalgebras and show how they arise as near-horizon geometries of certain half-BPS backgrounds or as a plan…
Study integrability of conformal geodesics on gravitational instantons.
problem Integrability of conformal geodesic flow on gravitational instantons.
method Analyzing conformal geodesic flow equations on SO(3)-invariant gravitational instantons, separating Hamilton-Jacobi equations, finding commuting first integrals, and using conformal Killing-Yano tensors. result First example of an integrable conformal geodesic flow on a non-symmetric four-manifold.
Establishes a connection between Kähler metrics and vector bundle sections.
problem Finding Kähler metrics in a conformal class.
method One-to-one correspondence between Kähler metrics and parallel sections of a vector bundle with conformally invariant connection.
result Obstructions for a Riemannian metric to be conformal to a Kähler metric.
Study on CKY forms on almost abelian Lie groups, proving parallelism and characterizing non-parallel cases.
problem Characterizing CKY forms on almost abelian Lie groups and proving parallelism.
method Analyzing almost abelian metric Lie algebras, proving parallelism for CKY forms, and classifying cases up to dimension 5.
result CKY forms are parallel on almost abelian Lie algebras, with exceptions for p=1 and p=n−1. The role of Killing and Killing-Yano tensors for studying the geodesic motion of the particle and the superparticle in a curved background is reviewed. Additionally the Papadopoulos list [74] for Killing-Yano tensors in G structures is reproduced by studying the torsion types these structures admit. The Papadopoulos li…
The study examines conditions for completeness and simplicity in hom-Lie superalgebras.
problem Conditions for completeness and simplicity in hom-Lie superalgebras.
method Equivalent conditions and derivations analysis.
result Conditions for completeness and simplicity in hom-Lie superalgebras.
The paper defines Z-graded hom-Lie superalgebras and explores their properties.
problem Understanding the structure and properties of Z-graded hom-Lie superalgebras.
method Definition and exploration of Z-graded hom-Lie superalgebras, invariant bilinear forms, and simplicity conditions.
result Maximal and minimal Z-graded hom-Lie superalgebras for local hom-Lie superalgebras are identified, and conditions for simplicity are checked.
New invariant for 3-manifolds from topological Hopf superalgebra.
problem Constructing an invariant for 3-manifolds.
method Using a ribbon superalgebra from a topological Hopf superalgebra, we construct an invariant of 3-manifolds of Hennings type.
result Constructs a new invariant for 3-manifolds from a topological Hopf superalgebra.
We give a detailed account of the geometric correspondence between a smooth complex projective quadric hypersurface Qn of dimension n≥3, and its twistor space PT, defined to be the space of all linear subspaces of maximal dimension of Qn. Viewing complex Euclidean space $\mat…
We present a maximally supersymmetric IIB string background. The geometry is that of a conformally flat lorentzian symmetric space G/K with solvable G, with a homogeneous five-form flux. We give the explicit supergravity solution, compute the isometries, the 32 Killing spinors, and the symmetry superalgebra, and then d…
Starting from the four normed division algebras - the real numbers, complex numbers, quaternions and octonions - a systematic procedure gives a 3-cocycle on the Poincare Lie superalgebra in dimensions 3, 4, 6 and 10. A related procedure gives a 4-cocycle on the Poincare Lie superalgebra in dimensions 4, 5, 7 and 11. In…
A notion of n-Lie algebra introduced by V.T. Filippov can be viewed as a generalization of a concept of binary Lie algebra to the algebras with n-ary multiplication law. A notion of Lie algebra can be extended to Z_2-graded structures giving a notion of Lie superalgebra. Analogously a notion of n-Lie algebra can be ext…
The paper introduces transposed Poisson superalgebras and their properties.
problem Developing algebraic structures for quantum physics.
method Defining transposed Poisson superalgebras using derivations and proving their identities.
result Six identities are crucial for understanding transposed Poisson superalgebras.
Study uses superalgebra homology to classify 4D Engel-like Lie algebras.
problem Classifying 4-dimensional Engel-like Lie algebras.
method Applied homology groups of Lie superalgebras.
result Distinguished and classified 4D Engel-like Lie algebras.
Recent work applying higher gauge theory to the superstring has indicated the presence of `higher symmetry'. Infinitesimally, this is realized by a `Lie 2-superalgebra' extending the Poincare superalgebra in precisely the dimensions where the classical supersymmetric string makes sense: 3, 4, 6 and 10. In the previous …
Study pseudo-Riemannian metrics on Jordan superalgebras.
problem No specific problem stated; focus on metrics.
method Coadjoint orbit-like construction for pseudo-Euclidean Jordan superalgebras.
result Investigated canonical pseudo-Riemannian metrics.
Classifies all toric Kahler surfaces with twistor 2-forms.
problem Classifying smooth 4-dimensional Kahler geometries with specific properties.
method Complete classification through algebraic and geometric analysis.
result Found six geometrically distinct families of toric Kahler surfaces.
Study Euler and Betti numbers of homology groups for a specific type of superalgebra.
problem Calculating Euler and Betti numbers for homology groups of pre Lie superalgebras.
method Introduced double weighted chain spaces to analyze pre Lie superalgebras of multi-vector fields with polynomial coefficients. Calculated Euler and Betti numbers for these homology groups.
result Derived formulas for Euler and Betti numbers of homology groups of pre Lie superalgebras.