arXiv research

New spinor types found on certain manifolds.

We study generalized Killing spinors on round spheres $\mathbb{S}^n$. We show that on the standard sphere $\mathbb{S}^8$ any generalized Killing spinor has to be an ordinary Killing spinor. Moreover we classify generalized Killing spinors on $\mathbb{S}^n$ whose associated symmetric endomorphism has at most two eigenva…

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

Study of higher spin Killing spinors on 3D manifolds, proving rigidity and providing explicit expressions.

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 imaginary generalized Spin$^c$ Killing spinors, providing that the dimension of t…

Classifies invariant generalised Killing spinors on Lie groups.

Study on hypersurfaces in Einstein manifolds using Killing spinors.

Study infinitesimal deformations of Killing spinors on nearly parallel G2-manifolds.

New spinorial field equation reveals geometric properties of Sasaki manifolds.

Extends symmetry superalgebras to include all hidden symmetries of manifolds.

We consider some natural infinitesimal Einstein deformations on Sasakian and 3-Sasakian manifolds. Some of these are infinitesimal deformations of Killing spinors and further some integrate to actual Killing spinor deformations. In particular, on 3-Sasakian 7 manifolds these yield infinitesimal Einstein deformations pr…

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

Spin geometry reviewed with applications in physics.

Study Killing equations for spinor-valued forms on pseudo-Riemannian manifolds.

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

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

This paper classifies 4D spin manifolds with skew Killing spinors.

Killing spinors help classify surfaces in complex projective plane.

Let $M$ be a pseudo-Riemannian spin manifold of dimension $n$ and signature $s$ and denote by $N$ the rank of the real spinor bundle. We prove that $M$ is locally homogeneous if it admits more than ${3/4}N$ independent Killing spinors with the same Killing number, unless $n\equiv 1 \pmod 4$ and $s\equiv 3 \pmod 4$. We …

New proof of stability for manifolds with imaginary Killing spinors.

Researchers derive symmetry operators from twistor spinors in curved spacetime.

This paper studies Sasakian quasi-Killing spinors on 3D Sasakian manifolds.

Classifies manifolds with specific spinors and constructs parallel spinors.

New framework for generalized Killing spinors on manifolds.

Odd-dimensional Riemannian manifolds admit pure spin-c Killing spinors if and only if they are α-Sasakian.

This text is dedicated to the real Killing equation on 3-dimensional Weyl manifolds. Any manifold admitting a real Killing spinor of weight 0 satisfies the conditions of a Gauduchon-Tod geometry. Conversely, any simply connected Gauduchon-Tod geometry has a 2-dimensional space of solutions of the real Killing equation …

Totally umbilical hypersurfaces in Spin^c manifolds with special spinors have constant mean curvature.

Extends Killing superalgebras to higher dimensions and signatures.

The paper constructs pseudo-Iwasawa solvmanifolds with Killing spinors.

Let $(M,ω)$ be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection $\nabla.$ Symplectic Killing spinor fields for this structure are sections of the symplectic spinor bundle satisfying a certain first order partial dif…

In this paper, we study the existence of a skew Killing spinor (see the definition below) on 2 and 3-dimensional Riemannian spin manifolds. We establish the integrability conditions and prove that these spinor fields correspond to twistor spinors in the two dimensional case while, up to a conformal change of the metric…

We describe and to some extent characterize a new family of Kähler spin manifolds admitting non-trivial imaginary Kählerian Killing spinors.

Defines Killing spinors and bosonic backgrounds in 5D supergravity.

Researchers classify harmful structures on unimodular Lie groups.

The paper finds exact solutions to a complex Einstein-Dirac-Maxwell system on 4D Sasakian spacetimes.

A supermanifold M is canonically associated to any pseudo Riemannian spin manifold (M_0,g_0). Extending the metric g_0 to a field g of bilinear forms g(p) on T_p M, p\in M_0, the pseudo Riemannian supergeometry of (M,g) is formulated as G-structure on M, where G is a supergroup with even part G_0\cong Spin(k,l); (k,l) …

We study generalized Killing spinors on compact Einstein manifolds with positive scalar curvature. This problem is related to the existence compact Einstein hypersurfaces in manifolds with parallel spinors, or equivalently, in Riemannian products of flat spaces, Calabi-Yau, hyperkaehler, G_2 and Spin(7) manifolds.

This paper classifies Killing superalgebras for Lorentzian 4-manifolds.

We outline the solution of the Killing spinor equations of the heterotic supergravity. In addition, we describe the classification of all half supersymmetric solutions.

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

We study the Einstein-Dirac equation as well as the weak Killing equation on Riemannian spin manifolds with codimension one foliation. We prove that, for any manifold $M^n$ admitting real Killing spinors (resp. parallel spinors), there exist warped product metrics $\barη$ on $M^n \times {\mathbb R}$ such that $(M^n \ti…

Spinorially constructs Sasakian and 3-Sasakian structures in arbitrary dimensions.

The study shows instability in certain Riemannian manifolds with real Killing spinors.

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 introducing the Killing equation for spinors of arbitrary weight, the result of A…

Extends Einstein Sasakian manifolds to new class with M-theory applications.

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 SU(5) or an (Spin(7)\ltimes R^8)x R structure, depending on whether the Killing vec…

We study the space of Killing fields on the four dimensional AdS spacetime $AdS^{3,1}$. Two subsets $\mathcal{S}$ and $\mathcal{O}$ are identified: $\mathcal{S}$ (the spinor Killing fields) is constructed from imaginary Killing spinors, and $\mathcal{O}$ (the observer Killing fields) consists of all hypersurface orthog…

Researchers calculate superalgebras for six-dimensional Lorentzian manifolds.