78 citations · 1.2k across the 112 of their papers we have counts for
8 papers · 2 filters
Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta
Vladimir S. Matveev
We describe all pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta. As an application, we solve the Beltrami problem…
Differential invariants for cubic integrals of geodesic flows on surfaces
Vladimir S. Matveev, Vsevolod V. Shevchishin
We construct differential invariants that vanish if and only if the geodesic flow of a 2-dimensional metric admits an integral of 3rd degree in momenta with a given Birkhoff-Koloko…
Gallot-Tanno Theorem for closed incomplete pseudo-Riemannian manifolds and applications
Vladimir S. Matveev, Pierre Mounoud
We extend the Gallot-Tanno Theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over a manifold admits a parallel symmetric tensor then it…
Gallot-Tanno theorem for closed incomplete pseudo-Riemannian manifolds and application
Pierre Mounoud
In this article we extend the Gallot-Tanno theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over such a manifold admits a parallel symmetric 2-…
Gallot-Tanno theorem for pseudo-Riemannian metrics and a proof that decomposable cones over closed complete pseudo-Riemannian manifolds do not exist
Vladimir S. Matveev
We generalize for pseudo-Riemannian metrics a classical result of Gallot and Tanno and use it to reprove a recent result of Alekseevsky, Cortes, Galaev and Leistner that decomposab…
There are no conformal Einstein rescalings of complete pseudo-Riemannian Einstein metrics
Volodymyr Kiosak, Vladimir S. Matveev
We prove the following statement: Let g be a light-line-complete pseudo-Riemannian Einstein metric of indefinite signature on a connected (n>2)-dimensional manifold M. Assume that…
Splitting and gluing constructions for geodesically equivalent pseudo-Riemannian metrics
Alexey V. Bolsinov, Vladimir S. Matveev
Two metrics and are geodesically equivalent, if they share the same (unparameterized) geodesics. We introduce two constructions that allow one to reduce many natural…
Compatibility of Gauss maps with metrics
J. Eschenburg, B. S. Kruglikov, V. S. Matveev +1
We give necessary and sufficient conditions on a smooth local map of a Riemannian manifold into the sphere to be the Gauss map of an isometric immersion …