A Gauss-Bonnet-Chern type obstruction for Killing vector fields on Lorentzian manifolds

2024/04/10 by Alfonso Romero, Miguel Sánchez, Romero, Alfonso +1
Mathematics · Physics and Astronomy · #53B30 #53C50 #53Z05 #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.2404.07284

openalex publication_date 2024/04/10 · openalex created_date 2024/04/13 · openalex updated_date 2026/08/01

Abstract

A new curvature obstruction to the existence of a timelike (resp. causal) Killing or homothetic vector field X on an even-dimensional (odd-dimensional) Lorentzian manifold, in terms of its timelike (resp. null) sectional curvature is given. As a consequence for the compact case, the well-known Gauss-Bonnet-Chern obstruction to the existence of semi-Riemannian metrics is extended from non-zero constant sectional curvature to non-zero timelike sectional curvature on X.

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