Indefinite Finsler Spaces and Timelike Spaces

1970/10/01 by John K. Beem · 9 citations
Physics and Astronomy · #Advanced Differential Geometry Research

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

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.

Cited by

• Finsler geometry as a model for relativistic gravity
• On the space of cone geodesics and positive paths of contactomorphisms
• Finsler metrics and relativistic spacetimes
• On the generalized m-Kropina metrics
• Concavity of spacetimes
• Foundations for a theory of emergent quantum mechanics and emergent classical gravity
• Characteristic tensors for almost Finsler manifolds
• Geometry of generalized higher order fields and applications to classical linear electrodynamics
• On the pseudo-Riemann's quartics in Finsler's geometry

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