Pure spinors, intrinsic torsion and curvature in odd dimensions

TAGHAVI-CHABERT, Arman. Pure spinors, intrinsic torsion and curvature in odd dimensions. Differential Geometry and its Applications. Amsterdam: Elsevier Science, 2017, roč. 51, April, s. 117-152. ISSN 0926-2245. Dostupné z: https://dx.doi.org/10.1016/j.difgeo.2017.02.008.

Základní údaje

• Originální název: Pure spinors, intrinsic torsion and curvature in odd dimensions
• Autoři: TAGHAVI-CHABERT, Arman (250 Francie, garant, domácí).
• Vydání: Differential Geometry and its Applications, Amsterdam, Elsevier Science, 2017, 0926-2245.

Další údaje

• Originální jazyk: angličtina
• Typ výsledku: Článek v odborném periodiku
• Obor: 10101 Pure mathematics
• Stát vydavatele: Nizozemské království
• Utajení: není předmětem státního či obchodního tajemství
• Impakt faktor: Impact factor: 0.760
• Kód RIV: RIV/00216224:14310/17:00094690
• Organizační jednotka: Přírodovědecká fakulta
• Doi: http://dx.doi.org/10.1016/j.difgeo.2017.02.008
• UT WoS: 000399856700011
• Klíčová slova anglicky: Complex Riemannian geometry; Pure spinors; Distributions; Intrinsic torsion; Curvature prescription; Spinorial equations
• Štítky: NZ, rivok
• Příznaky: Mezinárodní význam, Recenzováno

Anotace

We study the geometric properties of a $(2m + 1)$-dimensional complex manifold $M$ admitting a holomorphic reduction of the frame bundle to the structure group $P \subset Spin(2m + 1, C)$, the stabiliser of the line spanned by a pure spinor at a point. Geometrically, $M$ is endowed with a holomorphic metric $g$, a holomorphic volume form, a spin structure compatible with $g$, and a holomorphic pure spinor field $\xi$ up to scale. The defining property of $\xi$ is that it determines an almost null structure, i.e. an $m$-plane distribution $N_\xi$ along which $g$ is totally degenerate. We develop a spinor calculus, by means of which we encode the geometric properties of $N_\xi$ and of its rank-$(m + 1)$ orthogonal complement $N_\xi^\perp$ corresponding to the algebraic properties of the intrinsic torsion of the $P$-structure. This is the failure of the Levi-Civita connection $\nabla$ of $g$ to be compatible with the $P$ -structure. In a similar way, we examine the algebraic properties of the curvature of $\nabla$. Applications to spinorial differential equations are given. Notably, we relate the integrability properties of $N_\xi$ and $N_\xi^\perp$ to the existence of solutions of odd- dimensional versions of the zero-rest-mass field equation. We give necessary and sufficient conditions for the almost null structure associated to a pure conformal Killing spinor to be integrable. Finally, we conjecture a Goldberg–Sachs-type theorem on the existence of a certain class of almost null structures when $(M, g)$ has prescribed curvature. We discuss applications of this work to the study of real pseudo-Riemannian manifolds.

Návaznosti

• GP14-27885P, projekt VaV: Název: Skoro izotropní struktury v pseudo-riemannovské geometrii

Investor: Grantová agentura ČR, Skoro izotropní struktury v pseudo-riemannovské geometrii