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@article{1376706, author = {TaghaviandChabert, Arman}, article_number = {June}, doi = {http://dx.doi.org/10.1016/j.difgeo.2016.02.006}, keywords = {Complex Riemannian geometry; Pure spinors Distributions; Intrinsic torsion; Curvature prescription; Spinorial equations}, language = {eng}, issn = {0926-2245}, journal = {Differential Geometry and its Applications}, title = {Pure spinors, intrinsic torsion and curvature in even dimensions}, volume = {46}, year = {2016} }
TY - JOUR ID - 1376706 AU - Taghavi-Chabert, Arman PY - 2016 TI - Pure spinors, intrinsic torsion and curvature in even dimensions JF - Differential Geometry and its Applications VL - 46 IS - June SP - 164-203 EP - 164-203 PB - Elsevier Science SN - 09262245 KW - Complex Riemannian geometry KW - Pure spinors Distributions KW - Intrinsic torsion KW - Curvature prescription KW - Spinorial equations N2 - We study the geometric properties of a $2m$-dimensional complex manifold $M$ admitting a holomorphic reduction of the frame bundle to the structure group $P \subset Spin(2m, C)$, 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 $N_\xi$ 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. In particular, we give necessary and sufficient conditions for the almost null structure associated to a pure conformal Killing spinor to be integrable. We also 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. ER -
TAGHAVI-CHABERT, Arman. Pure spinors, intrinsic torsion and curvature in even dimensions. \textit{Differential Geometry and its Applications}. Elsevier Science, 2016, roč.~46, June, s.~164-203. ISSN~0926-2245. Dostupné z: https://dx.doi.org/10.1016/j.difgeo.2016.02.006.
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