Pseudo-Riemannian manifolds with common geodesics. (English. Russian original) Zbl 0933.53002

Aminova, A. V.

Russ. Math. Surv. 48, No. 2, 105-160 (1993); translation from Usp. Mat. Nauk 48, No. 2(290), 107-164 (1993).

This paper is devoted to the classical geometric problem of determining pseudo-Riemannian metrics \(g\) and \(g'\) that have corresponding geodesics. This problem arises in relation with a problem in dynamics, concerning transformations of the equations of motion that preserve trajectories.
The paper comprises four chapters: (I) “Projective connections and projective mappings”, (II) “Projectively equivalent Riemannian connections”, (III) “Pseudo-Riemannian metrics with common geodesics”, and (IV) “Pseudo-Riemannian metrics with general connections”.
The list of references contains 111 entries.

MSC:

53-02	Research exposition (monographs, survey articles) pertaining to differential geometry
53C22	Geodesics in global differential geometry
53B30	Local differential geometry of Lorentz metrics, indefinite metrics

Keywords:

projective connections; projective mappings