Related papers: Killing spinor-valued forms and the cone construct…

This paper deals with the classification of spinor fields according to the bilinear covariants in 7 dimensions. The previously investigated Riemannian case is characterized by either one spinor field class, in the real case of Majorana…

For any manifold M, the direct sum TM \oplus T*M carries a natural inner product given by the pairing of vectors and covectors. Differential forms on M may be viewed as spinors for the corresponding Clifford bundle, and in particular there…

The techniques of spinorial geometry are used to classify solutions admitting Killing spinors in the theory of minimal anti-de Sitter $N=2$, $D=4$ supergravity, where the gauge kinetic term comes with the opposite sign. There are four…

We calculate the relevant Spencer cohomology of the minimal Poincar\'e superalgebra in 5 spacetime dimensions and use it to define Killing spinors via a connection on the spinor bundle of a 5-dimensional lorentzian spin manifold. We give a…

We construct explicit examples of non-relativistic supersymmetric field theories on curved Newton-Cartan three-manifolds. These results are obtained by performing a null reduction of four-dimensional supersymmetric field theories on…

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 present a set of equations for a 4D Killing spinor which guarantees the Seiberg-Witten theories on a curved background to be supersymmetric. The equations involve an SU(2) gauge field and some auxiliary fields in addition to the metric.…

The connection between differential geometry of curves and the (2+1)-dimensional integrable spin system - the M-III equation is established. Using the presented geometrical formalism the L-equivalent counterpart of the M-III equation is…

We present definitions and properties of conformal Killing, Killing and planarity forms on a Riemannian manifold and determine Tachibana, Killing and planarity numbers as an analog of the well known Betti numbers. We state some set of…

We investigate the implications of the existence of Killing spinors in a spacetime. In particular, we show that in vacuum and electrovacuum a Killing spinor, along with some assumptions on the associated Killing vector in an asymptotic…

We show necessary conditions for the existence of transversal Killing spinors on a spin manifold endowed with a Riemannian flow.

Hano's theorem states that the space of Killing vector fields of a complete simply connected Riemannian manifold is isomorphic to the direct sum of the Killing vector fields of the factors in its de Rham decomposition. We prove a…

Starting from a nonlinear realisation of eleven dimensional supergravity based on the group G11, whose generators appear as low level generators of E11, we present a super extended algebra, which leads to a covariant derivative of spinors…

Methods are presented for finding Killing-Yano tensors, conformal Killing-Yano tensors, and conformal Killing vectors in spacetimes with a hypersurface orthogonal Killing vector. These methods are similar to a method developed by the…

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…

An approximate Killing field may be defined on a compact, Riemannian geometry by solving an eigenvalue problem for a certain elliptic operator. This paper studies the effect of small perturbations in the Riemannian metric on the resulting…

For supersymmetric spacetimes in eleven dimensions admitting a null Killing spinor, a set of explicit necessary and sufficient conditions for the existence of any number of arbitrary additional Killing spinors is derived. The necessary and…

The assumption in the main result of [Peter W. Michor: Basic Differential Forms for Actions of Lie Groups, Proc. AMS 124, 5 (1996) 1633-1642] is removed. Thus: A section of a Riemannian $G$-manifold $M$ is a closed submanifold $\Si$ which…

We describe the different classes of $\mathrm{Spin(7)}$ structures in terms of spinorial equations. We relate them to the spinorial description of $\mathrm{G}_2$ structures in some geometrical situations. Our approach enables us to analyze…

We solve the Killing spinor equations of standard and massive IIA supergravities for a Killing spinor whose isotropy subgroup in Spin(9, 1) is SU(4) and identify the geometry of the spacetime. We demonstrate that the Killing spinor…