Indefinite Finsler Spaces and Timelike Spaces

1970/10/01 by John K. Beem · 115 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Computer science #Generalization #Geometry #Lorentz transformation #Mathematical analysis #Mathematics #Metric space #Physics #Pure mathematics #Signature (topology) #Space (punctuation) #Tensor (intrinsic definition)

paper · pdf · doi:10.4153/cjm-1970-119-7

published in Canadian Journal of Mathematics 22(5), 1035-1039 (Cambridge University Press)

openalex publication_date 1970/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

In this paper we investigate indefinite Finsler spaces in which the metric tensor has signature n — 2. These spaces are a generalization of Lorentz manifolds. Locally a partial ordering may be defined such that the reverse triangle inequality holds for this partial ordering. Consequently, the spaces we study may be made into what Busemann [ 3 ] terms locally timelike spaces. Furthermore, sufficient conditions are obtained for an indefinite Finsler space to be a doubly timelike surface (see [ 2; 4 ]). In particular, all two-dimensional pseudo-Riemannian spaces are shown to be doubly timelike surfaces.

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• On the pseudo-Riemann's quartics in Finsler's geometry
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• Comparison theorems on weighted Finsler manifolds and spacetimes with ε-range
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