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We construct a concrete example of constant Gauss curvature K = 1 on the 2-sphere having all geodesics closed and of same length. [ABSTRACT FROM AUTHOR]

Special coordinate systems are constructed in a neighborhood of a point or of a curve. Taylor expansions can then be easily inferred for the metric, the connection, or the Finsler Lagrangian in terms of curvature invariants. These coordinates circumvent the difficulties of the normal and Fermi coordinates in Finsler geometry, which in general are not sufficiently differentiable. They are obtained applying the usual constructions to the pullback of a horizontally torsionless connection. The results so obtained are easily specialized to the Berwald or Chern–Rund connections and have application in the study of the equivalence principle in Finslerian extensions of general relativity. [ABSTRACT FROM AUTHOR]

An extension of conformal equivalence for Finsler metrics is introduced and called weakly conformal equivalence and is used to define the weakly conformal transformations. The conformal Lichnerowicz-Obata conjecture is refined to weakly conformal Finsler geometry. It is proved that: If X is a weakly conformal complete vector field on a connected Finsler space ( M, F) of dimension [ABSTRACT FROM AUTHOR]