2023/01/10 by Matthias Hammerl, Katja Sagerschnig, Hammerl, Matthias +5
Mathematics · Physics and Astronomy · #53A20 #53A30 #53B30 #53C07 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2301.04238
openalex publication_date 2023/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a geometric construction and characterization of 2n-dimensional split-signature conformal structures endowed with a twistor spinor with integrable kernel. The construction is regarded as a modification of the conformal Patterson--Walker metric construction for n-dimensional projective manifolds. The characterization is presented in terms of the twistor spinor and an integrability condition on the conformal Weyl curvature. We further derive complete description of Einstein metrics and infinitesimal conformal symmetries in terms of suitable projective data. Finally, we obtain an explicit geometrically constructed Fefferman--Graham ambient metric and show vanishing of Q-curvature.