In pseudo-Riemannian geometry the spaces of space-like and time-like geodesics on a
pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian …

The paper surveys open problems and questions related to geodesics defined by
Riemannian, Finsler, semi-Riemannian and magnetic structures on manifolds. It is an …

We show that the following two separately developed theories, the theory of Benenti systems
in mathematical physics and the theory of projectively equivalent metrics in classical …

We construct all orthogonal separating coordinates in constant curvature spaces of arbitrary
signature. Further, we construct explicit transformation between orthogonal separating and …

We suggest a construction that, given an orbital diffeomorphism between two Hamiltonian
systems, produces integrals of them. We treat geodesic equivalence of metrics as the main …

Mathematische Annalen Page 1 Math. Ann. (2008) 340:437–463 DOI 10.1007/s00208-007-0158-3
Mathematische Annalen A solution of a problem of Sophus Lie: normal forms of two-dimensional …

PROOF OF THE PROJECTIVE LICHNEROWICZ-OBATA CONJECTURE Vladimir S. Matveev
Abstract 1. Introduction 1.1. Results. Definition 1. L Page 1 j. differential geometry 75 (2007) …

Complete Einstein Metrics are Geodesically Rigid Page 1 Digital Object Identifier (DOI)
10.1007/s00220-008-0719-7 Commun. Math. Phys. 289, 383–400 (2009) Communications in …

Two pseudo-Riemannian metrics $ g $ and $\bar g $ are geodesically equivalent if they
share the same (unparameterized) geodesics. We give a complete local description of such …

We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the
first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian …