1997/08/05 by Friedrich W. Hehl, Hehl, Friedrich W., Uwe Muench +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Computer science #Connection (principal bundle) #Cosmology and Gravitation Theories #Curvature #Differentiable function #FOS: Physical sciences #Fundamental theorem of Riemannian geometry #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry #Information geometry #Levi-Civita connection #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Metric (unit) #Metric connection #Metric space #Physics #Point (geometry) #Pseudo-Riemannian manifold #Pure mathematics #Quantum mechanics #Riemannian geometry #Riemannian manifold #Scalar curvature #Space (punctuation) #Spacetime #Statistical manifold #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9708007
3 pages, LaTeX, no figures, reply to gr-qc/9706068
arxiv created 1997/08/05 · openalex publication_date 1997/08/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A four-dimensional differentiable manifold is given with an arbitrary linear connection Γαβ=Γiαβdxi. Megged has claimed that he can define a metric Gαβ by means of a certain integral equation such that the connection is compatible with the metric. We point out that Megged's implicite definition of his metric Gαβ is equivalent to the assumption of a vanishing nonmetricity. Thus his result turns out to be trivial.