Related papers: Killing spinor-valued forms and their integrabilit…
We construct invariants for bosonic and spinning tensionless (null) strings in backgrounds that carry Killing tensors or Killing-Yano tensors of mixed type. This is facilitated by the close relation of these strings to point particles. We…
We solve the Killing spinor equations and determine the near horizon geometries of M-theory that preserve at least one supersymmetry. The M-horizon spatial sections are 9-dimensional manifolds with a Spin(7) structure restricted by…
In this paper, the Dirac, twistor and Killing equations on Weyl manifolds with CSpin structures are investigated. A conformal Schr"odinger-Lichnerowicz formula is presented and used to show integrability conditions for these equations. By…
In this note we give an explicit formula for the preserved Killing spinors in deformed string theory backgrounds corresponding to integrable Yang--Baxter deformations realized via (sequences of) TsT transformations. The Killing spinors can…
The second order Killing and conformal tensors are analyzed in terms of their spectral decomposition, and some properties of the eigenvalues and the eigenspaces are shown. When the tensor is of type I with only two different eigenvalues,…
Generalization of twistor spinors to K\"ahler manifolds which are called K\"ahlerian twistor spinors are considered. We find the differential equation satisfied by the bilinear forms of K\"ahlerian twistor spinors. We show that the bilinear…
We study twistor forms on products of compact Riemannian manifolds and show that they are defined by Killing forms on the factors. The main result of this note is a necessary step in the classification of compact Riemannian manifolds with…
We study the Minkowski formula of conformal Killing-Yano two-forms in a spacetime of constant curvature. We establish the spacetime Alexandrov theorem with a free boundary.
The invariant theory of Killing tensors (ITKT) is extended by introducing the new concepts of covariants and joint invariants of (product) vector spaces of Killing tensors defined in pseudo-Riemannian spaces of constant curvature. The…
We characterize the $2$-Killing vector fields on a multiply twisted product manifold, with a special view towards generalized spacetimes. More precisely, we determine the nonlinear differential equations that completely describe them and…
Motivated by the study of Killing forms on compact Riemannian manifolds of negative sectional curvature, we introduce the notion of generalized vector cross products on $\mathbb{R}^n$ and give their classification. Using previous results…
We present a complete classification of invariant generalised Killing spinors on three-dimensional Lie groups. We show that, in this context, the existence of a non-trivial invariant generalised Killing spinor implies that all invariant…
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…
In general, geometries of Petrov type II do not admit symmetries in terms of Killing vectors or spinors. We introduce a weaker form of Killing equations which do admit solutions. In particular, there is an analog of the Penrose-Walker…
We provide a general method for studying manifestly $O(n+1)$ covariant formulation of $p$-form gauge theories by stereographically projecting these theories, defined in flat Euclidean space, onto the surface of a hypersphere. The gauge…
We have found generic Killing spinor identities which bosonic equations of motion have to satisfy in supersymmetric theories if the solutions admit Killing spinors. Those identities constrain possible quantum corrections to bosonic…
We solve the Killing spinor equations of 6-dimensional (1,0) superconformal theories in all cases. In particular, we derive the conditions on the fields imposed by the Killing spinor equations and demonstrate that these depend on the…
We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This…
BGG-equations are geometric overdetermined systems of PDEs on parabolic geometries. Normal solutions of BGG-equations are particularly interesting and we give a simple formula for the necessary and sufficient additional integrability…
We employ the G-structure formalism to study supersymmetric solutions of minimal and SU(2) gauged supergravities in seven dimensions admitting Killing spinors with associated timelike Killing vector. The most general such Killing spinor…