arXiv research

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…

Researchers develop new symmetry operators from conformal Killing-Yano forms.

Study Minkowski formula for conformal Killing-Yano 2-forms in constant curvature spacetimes.

Harmonic spinors linked to twistor spinors via potential forms and conformal Killing-Yano forms.

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…

Study BGG operators on homogeneous conformal geometries.

Killing-Yano and conformal Killing-Yano superalgebras are rigid in constant curvature manifolds.

We show that the Euclidean Kerr-NUT-(A)dS metric in $2m$ dimensions locally admits $2^m$ 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…

Estimates quasi-local mass using Minkowski formula and conformal Killing-Yano forms.

Researchers derive symmetry operators from twistor spinors in curved spacetime.

The study generalizes twistor spinors to Kähler manifolds and finds bilinear form equations.

Researchers describe a method to construct Ricci-flat metrics on a specific surface.

We show the existence of conformal Killing-Yano tensors on a manifold endowed with a mixed 3-Sasakian structure.

Study invariant CKY 2-forms on 5D Lie groups, classifying and determining their properties.

Extended superalgebras from twistor and Killing spinors in constant curvature and Einstein manifolds.

Study finds only complex 2-step nilpotent Lie groups have Killing-Yano forms.

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…

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…

Study on CKY forms on almost abelian Lie groups, proving parallelism and characterizing non-parallel cases.

Extends symmetry superalgebras to include all hidden symmetries of manifolds.

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…

Classifies all toric Kahler surfaces with twistor 2-forms.

Study finds necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.

The paper develops a comprehensive theory of submanifolds in conformal geometries.

Establishes a connection between Kähler metrics and vector bundle sections.

Study finds all hyper-Kähler 4-manifolds with specific symmetries and structures.

We give a detailed account of the geometric correspondence between a smooth complex projective quadric hypersurface $\mathcal{Q}^n$ of dimension $n \geq 3$, and its twistor space $\mathbb{PT}$, defined to be the space of all linear subspaces of maximal dimension of $\mathcal{Q}^n$. Viewing complex Euclidean space $\mat…

It has been shown that for each Killing-Yano (KY)-form accepted by an $n$-dimensional (pseudo)Riemannian manifold of arbitrary signature, two basic gravitational currents can be defined. Conservation of the currents are explicitly proved by showing co-exactness of the one and co-closedness of the other. Some general ge…

Spin geometry reviewed with applications in physics.

Estimates eigenvalues of modified Dirac operators with multi-forms.

New currents derived from Killing-Yano tensors for gravity.

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…

The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codim…

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…

Study integrability of conformal geodesics on gravitational instantons.

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…

Study of Killing spinor-valued forms and their integrability conditions.

The Teukolsky connection is linked to a complex structure on Einstein spacetimes.

We discuss a deformation of Sasakian structure in the presence of totally skew-symmetric torsion by introducing odd dimensional manifolds whose metric cones are Kähler with torsion. It is shown that such a geometry inherits similar properties to those of Sasakian geometry. As an example of them, we present an explicit …

Classifies conformal Killing 3-forms on nearly Kähler manifolds.

The paper examines conditions for conformal Ricci solitons on generalized ($κ, μ$)-space forms.

Study proves higher-order conformal forms don't exist in odd dimensions.

Conformal Killing forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We show the existence of conformal Killing forms on nearly Kaehler and weak G_2-manifolds. Moreover, we give a…

Researchers solve conformal Killing forms on Kaehler manifolds.

New conformally invariant forms help identify Einstein metrics.

Study characterizes conformal boundaries of de Sitter spacetimes.

Study classifies manifolds with nonpositive curvature and finds conformal Killing forms.

We construct a conformally invariant vector bundle connection such that its equation of parallel transport is a first order system that gives a prolongation of the conformal Killing equation on differential forms. Parallel sections of this connection are related bijectively to solutions of the conformal Killing equatio…