Hyperbolic angles in Lorentzian length spaces and timelike curvature bounds

Author:

Beran Tobias1,Sämann Clemens1

Affiliation:

1. Faculty of Mathematics University of Vienna Vienna Austria

Abstract

AbstractWithin the synthetic‐geometric framework of Lorentzian (pre‐)length spaces developed in Kunzinger and Sämann (Ann. Glob. Anal. Geom. 54 (2018), no. 3, 399–447) we introduce a notion of a hyperbolic angle, an angle between timelike curves and related concepts such as timelike tangent cone and exponential map. This provides valuable technical tools for the further development of the theory and paves the way for the main result of the article, which is the characterization of timelike curvature bounds (defined via triangle comparison) with an angle monotonicity condition. Further, we improve on a geodesic non‐branching result for spaces with timelike curvature bounded below.

Funder

Austrian Science Fund

Publisher

Wiley

Subject

General Mathematics

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1. On curvature bounds in Lorentzian length spaces;Journal of the London Mathematical Society;2024-07-30

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