Characterizing Finsler spaces which are pseudo-Riemannian of constant curvature

John Kelly Beem

Vol. 64 (1976), No. 1, 67–77

DOI: 10.2140/pjm.1976.64.67

Abstract

Let M be an indefinite Finsler space. The bisector of two points of M is the set of points equidistant from these two points. A bisector is called flat if with any pair of points it contains the extremals joining this pair. In this paper it is shown that M is pseudo-Riemannian of constant curvature if and only if M locally has flat bisectors. Another result is that M is pseudo-Riemannian of constant curvature if and only if M can be reflected locally in each nonnull extremal.

Mathematical Subject Classification 2000

Primary: 53B40

Milestones

Received: 9 July 1974

Revised: 30 January 1976

Published: 1 May 1976