Équations différentielles caractéristiques de la sphère

Gallot, Sylvestre

doi:10.24033/asens.1366

Cited by 79 publications

(111 citation statements)

References 2 publications

(2 reference statements)

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“…The characterisation due to Bär [49] establishes that R admits a Killing spinor (with imaginary Killing constant) if and only if C(R) admits a parallel spinor. If R is complete, it follows from [47,53] that Hol ∇ (C(R)) must be either SU( r+1 2 ), Sp( r+1 4 ), G 2 (if r = 6), Spin(7) (if r = 7) or trivial. In these cases, R is respectively Einstein-Sasakian, 3-Sasakian, nearly Kähler, weak G 2 or a sphere.…”

Section: If ε Is Not Parallel Then M Is Locally Isometric To Eithermentioning

confidence: 99%

Conformal symmetry superalgebras

Medeiros

Hollands

2013

Class. Quantum Grav.

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ABSTRACT. We show how the rigid conformal supersymmetries associated with a certain class of pseudo-Riemannian spin manifolds define a Lie superalgebra. The even part of this superalgebra contains conformal isometries and constant R-symmetries. The odd part is generated by twistor spinors valued in a particular R-symmetry representation. We prove that any manifold which admits a conformal symmetry superalgebra of this type must generically have dimension less than seven. Moreover, in dimensions three, four, five and six, we provide the generic data from which the conformal symmetry superalgebra is prescribed. For conformally flat metrics in these dimensions, and compact R-symmetry, we identify each of the associated conformal symmetry superalgebras with one of the conformal superalgebras classified by Nahm. We also describe several examples for Lorentzian metrics that are not conformally flat.

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Section: If ε Is Not Parallel Then M Is Locally Isometric To Eithermentioning

confidence: 99%

Conformal symmetry superalgebras

Medeiros

Hollands

2013

Class. Quantum Grav.

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“…We will moreover assume that X is simply connected. This allows us to use a result of Gallot's [6] quoted in [4], which says that the cone over a compact simply-connected manifold is either flat, so that the manifold is the round sphere, or irreducible. Finally, the simply-connected irreducible manifolds admitting parallel spinors have been classified by Wang [18].…”

Section: Killing Spinors and Parallel Spinorsmentioning

confidence: 99%

On the supersymmetries of anti-de Sitter vacua

Figueroa-O’Farrill

1999

Class. Quantum Grav.

103

166

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“…Besides providing an important step in the proof of Theorem 1, Theorem 5 could be interesting on its own since investigation of parallel tensor fields on cone manifolds is a classical topic, see for example [1,6,21].…”

Section: 4mentioning

confidence: 99%

Degree of mobility for metrics of Lorentzian signature and parallel (0,2)-tensor fields on cone manifolds

Fedorova

Matveev

2013

Proceedings of the London Mathematical Society

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Abstract. Degree of mobility of a (pseudo-Riemannian) metric is the dimension of the space of metrics geodesically equivalent to it. We describe all possible values of the degree of mobility on a simply connected n-dimensional manifold of lorentz signature. As an application we calculate all possible differences between the dimension of the projective and the isometry groups. One of the main new technical results in the proof is the description of all parallel symmetric (0, 2)-tensor fields on cone manifolds of signature (n − 1, 2).

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Équations différentielles caractéristiques de la sphère

Cited by 79 publications

References 2 publications

Conformal symmetry superalgebras

Conformal symmetry superalgebras

On the supersymmetries of anti-de Sitter vacua

Degree of mobility for metrics of Lorentzian signature and parallel (0,2)-tensor fields on cone manifolds

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