2008/12/31 by Mihaela Pilca · 9 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Curvature #Differential geometry #Differential operator #Dirac operator #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Mathematical analysis #Mathematical physics #Mathematics #Pure mathematics #Scalar (mathematics) #Scalar curvature #Spinor #Twistor space #Twistor theory #math.DG #msc:53C25 #msc:53C55 #msc:58J50
paper · pdf · doi:10.1007/s00209-010-0668-7
published in Mathematische Zeitschrift 268(1-2), 223-255 (Springer Science+Business Media) · shorter version; to appear in Math.Z
openalex publication_date 2010/01/27 · arxiv created 2010/02/01 · arxiv updated 2010/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
On a Kähler spin manifold Kählerian twistor spinors are a natural analogue of twistor spinors on Riemannian spin manifolds. They are defined as sections in the kernel of a first order differential operator adapted to the Kähler structure, called Kählerian twistor (Penrose) operator. We study Kählerian twistor spinors and give a complete description of compact Kähler manifolds of constant scalar curvature admitting such spinors. As in the Riemannian case, the existence of Kählerian twistor spinors is related to the lower bound of the spectrum of the Dirac operator.