Three-dimensional manifolds having metrics with the same geodesics.

DOI10.1016/S0040-9383(03)00004-1zbMath1035.53117MaRDI QIDQ1398217

Vladimir S. Matveev

Publication date: 29 July 2003

Published in: Topology (Search for Journal in Brave)

zbMATH Keywords

Lens spaceIntegrable systemStäckel systemLiouville metricGeodesic equivalenceGeodesic rigidityLocal product structureObstructions to integrabilityProjective connectionProjectively equivalent metricsSeparation of variables

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Geodesics in global differential geometry (53C22) Rigidity results (53C24) Geodesic flows in symplectic geometry and contact geometry (53D25)

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What does a vector field know about volume? ⋮ Quantum integrability for the Beltrami-Laplace operators of projectively equivalent metrics of arbitrary signatures ⋮ Two-dimensional metrics admitting precisely one projective vector field ⋮ On the number of nontrivial projective transformations of closed manifolds ⋮ Splitting and gluing lemmas for geodesically equivalent pseudo-Riemannian metrics ⋮ Proof of the projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two ⋮ Complete Einstein metrics are geodesically rigid ⋮ Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta ⋮ Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta, and proof of the projective Obata conjecture for two-dimensional pseudo-Riemannian metrics ⋮ Vanishing of the entropy pseudonorm for certain integrable systems ⋮ Open problems and questions about geodesics

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