Related papers: Spinor bilinears and Killing-Yano forms in general…
We define the notion of a Killing (super)algebra for a connection on a spinor bundle associated to a generalised spin structure on a pseudo-Riemannian manifold of any signature. We are led naturally to include in the even subspace not only…
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…
We investigate the Killing spinor equations of IIB supergravity for one Killing spinor. We show that there are three types of orbits of Spin(9,1) in the space of Weyl spinors which give rise to Killing spinors with stability subgroups…
The Rainich problem for the Killing-Yano tensors posed by Collinson \cite{col} is solved. In intermediate steps, we first obtain the necessary and sufficient conditions for a 2+2 almost-product structure to determine the principal 2--planes…
In this paper we give a spinorial representation of submanifolds of any dimension and codimension into Riemannian space forms in terms of the existence of so called generalized Killing spinors. We then discuss several applications, among…
In the main part of this thesis, we present the foundations and initial results of the Spinorial Geometry formalism for solving Killing spinor equations. This method can be used for any supergravity theory, although we largely focus on D=11…
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields,…
We propose a way to classify all supersymmetric configurations of D=11 supergravity using the G-structures defined by the Killing spinors. We show that the most general bosonic geometries admitting a Killing spinor have at least a local…
Following the program of investigation of alternative spinor duals potentially applicable to fermions beyond the standard model, we demonstrate explicitly the existence of several well-defined spinor duals. Going further we define a mapping…
We characterize certain CR structures of arbitrary codimension (different from 3, 4 and 5) on Riemannian Spin$^c$ manifolds by the existence of a Spin$^c$ structure carrying a strictly partially pure spinor field. Furthermore, we study the…
The higher order symmetries are investigated in a covariant Hamiltonian formulation. The covariant phase-space approach is extended to include the presence of external gauge fields and scalar potentials. The special role of the Killing-Yano…
We review some aspects of the spinorial geometry approach to the classification of supersymmetric solutions of supergravity theories. In particular, we explain how spinorial geometry can be used to express the Killing spinor equations in…
A geometric formulation of the Lax pair equation on a curved manifold is studied using phase space formalism. The corresponding (covariantly conserved) Lax tensor is defined and the method of generation of constants of motion from it is…
We give a spinorial characterization of isometrically immersed surfaces into 3-dimensional homogeneous manifolds with 4-dimensional isometry group in terms of the existence of a particular spinor, called generalized Killing spinor. This…
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…
A 3+1 decomposition of the twistor and valence-2 Killing spinor equation is made using the space spinor formalism. Conditions on initial data sets for the Einstein vacuum equations are given so that their developments contain solutions to…
We discuss novel generalisations of Killing tensors, which are introduced by considering rational first integrals of geodesic equations. We introduce the notion of inconstructible generalised Killing tensors, which cannot be constructed…
In this paper, we extend the study of generalized Killing spinors on Riemannian Spin$^c$ manifolds started by Moroianu and Herzlich to complex Killing functions. We prove that such spinor fields are always real Spin$^c$ Killing spinors or…
In this paper we initiate a classification of local metrics admitting the principal Killing--Yano tensor with a skew-symmetric torsion. It is demonstrated that in such spacetimes rank-2 Killing tensors occur naturally and mutually commute.…
After reviewing the Lounesto spinor field classification, according to the bilinear covariants associated to a spinor field, we call attention and unravel some prominent features involving unexpected properties about spinor fields under…