# Killing spinors and related symmetries in six dimensions

@article{Batista2015KillingSA, title={Killing spinors and related symmetries in six dimensions}, author={Carlos Batista}, journal={Physical Review D}, year={2015}, volume={93}, pages={065002} }

Benefiting from the index spinorial formalism, the Killing spinor equation is integrated in six-dimensional spacetimes. The integrability conditions for the existence of a Killing spinor are worked out and the Killing spinors are classified into two algebraic types; in the first type the scalar curvature of the spacetime must be negative, while in the second type the spacetime must be an Einstein manifold. In addition, the equations that define Killing-Yano (KY) and closed conformal Killing…

## 3 Citations

### Spinorial Formalism and Symmetries in Six Dimensions

- Physics
- 2019

Spinors are objects that carry the fundamental representation of the orthogonal gourp associated to a metric. Thus, in any space endowed with a metric one can introduce spinorial calculus as a useful…

### Two-Component Spinorial Formalism Using Quaternions for Six-Dimensional Spacetimes

- MathematicsAdvances in Applied Clifford Algebras
- 2021

In this article we construct and discuss several aspects of the two-component spinorial formalism for six-dimensional spacetimes, in which chiral spinors are represented by objects with two…

### The spinorial formalism, with applications in physics

- Physics
- 2017

SILVA FILHO, Carlos Alberto Batista da, tambem e conhecido em citacoes bibliograficas por: BATISTA, Carlos

## 53 References

### On the six-dimensional Kerr theorem and twistor equation

- Mathematics
- 2014

The Kerr theorem is revisited as part of the twistor program in six dimensions. The relationship between pure spinors and integrable 3-planes is investigated. The real condition for Lorentzian…

### The spinorial geometry of supersymmetric backgrounds

- Mathematics, Physics
- 2004

We propose a new method to solve the Killing spinor equations of 11-dimensional supergravity based on a description of spinors in terms of forms and on the Spin(1, 10) gauge symmetry of the…

### Spinor calculus on five-dimensional spacetimes

- Physics, Mathematics
- 2009

Penrose’s spinor calculus of four-dimensional Lorentzian geometry is extended to the case of five-dimensional Lorentzian geometry. Such fruitful ideas in Penrose’s spinor calculus as the spin…

### Geometry of Killing spinors in neutral signature

- Mathematics
- 2015

We classify the supersymmetric solutions of minimal N = 2 gauged supergravity in four dimensions with neutral signature. They are distinguished according to the sign of the cosmological constant and…

### Integrability conditions for Killing spinors

- Physics
- 1984

The conditions for the existence of solutions ofDµη=±cγµη are discussed. In general, it is not sufficient to consider only the first integrability condition [Dµ,Dv]η=−2c2γ{µv}η; in particular, the…

### Conformally invariant spinorial equations in six dimensions

- Mathematics
- 2015

This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretations are worked out.…

### Hidden symmetries and supergravity solutions

- Physics
- 2012

The role of Killing and Killing-Yano tensors for studying the geodesic motion of the particle and the superparticle in a curved background is reviewed. Additionally, the Papadopoulos list [G.…

### Spinors and the Weyl tensor classification in six dimensions

- Mathematics
- 2013

A spinorial approach to six-dimensional differential geometry is constructed and used to analyze tensor fields of low rank, with special attention to the Weyl tensor. We perform a study similar to…

### All supersymmetric solutions of minimal gauged supergravity in ﬁve dimensions

- Physics

All purely bosonic supersymmetric solutions of minimal gauged supergravity in ﬁve dimensions are classiﬁed. The solutions fall into two classes depending on whether the Killing vector constructed…