arXiv research

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…

Study on hypersurfaces in Einstein manifolds using Killing spinors.

New framework for generalized Killing spinors on manifolds.

New proof of stability for manifolds with imaginary Killing spinors.

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 …

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

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

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

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 spinor types found on certain manifolds.

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…

Study of four-dimensional Lorentzian manifolds with real Killing spinors.

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

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

New spinor fields reveal local or global geometric properties of manifolds.

New spinorial field equation reveals geometric properties of Sasaki manifolds.

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…

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…

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

On a Lorentzian manifold the existence of a parallel null vector field implies certain constraint conditions on the induced Riemannian geometry of a space-like hypersurface. We will derive these constraint conditions and, conversely, show that every real analytic Riemannian manifold satisfying the constraint conditions…

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

Classifies invariant generalised Killing spinors on Lie groups.

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…

We study the intrinsic geometry of hypersurfaces in Calabi-Yau manifolds of real dimension 6 and, more generally, SU(2)-structures on 5-manifolds defined by a generalized Killing spinor. We prove that in the real analytic case, such a 5-manifold can be isometrically embedded as a hypersurface in a Calabi-Yau manifold i…

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

Classifies manifolds with specific spinors and constructs parallel spinors.

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

Study shows deformation of nearly Kähler manifolds is obstructed.

Study on deformation theory of nearly G2 manifolds with obstructions.

We prove that a smooth Riemannian manifold admitting an imaginary generalized Killing spinor whose Dirac current satisfies an additional algebraic constraint condition can be embedded as spacelike Cauchy hypersurface in a smooth Lorentzian manifold on which the given spinor extends to a null parallel spinor. This is in…

Simply connected 3-dimensional homogeneous manifolds $E(κ, τ)$, with 4-dimensional isometry group, have a canonical Spin$^c$ structure carrying parallel or Killing spinors. The restriction to any hypersurface of these parallel or Killing spinors allows to characterize isometric immersions of surfaces into $E(κ, τ)$. As…

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

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.

Spin geometry reviewed with applications in physics.

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

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

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

This paper classifies Killing superalgebras for Lorentzian 4-manifolds.

The paper constructs pseudo-Iwasawa solvmanifolds with Killing spinors.

Defines Killing spinors and bosonic backgrounds in 5D supergravity.

Study on instantons on cylinder manifolds with specific conditions.

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…

Researchers study Killing superalgebras in 2D manifolds.

Researchers classify harmful structures on unimodular Lie groups.

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…

We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifo…

Researchers calculate superalgebras for six-dimensional Lorentzian manifolds.