GEOMETRIC EXPLANATION OF THE BELTRAMI THEOREM

DOI10.1142/S0219887806001296zbMath1095.53023WikidataQ126077244 ScholiaQ126077244MaRDI QIDQ5484706

Vladimir S. Matveev

Publication date: 21 August 2006

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

zbMATH Keywords

projective transformationsprojectively equivalent metricsgeodesically equivalent metricsBeltrami theoremquadratic integrals of the geodesic flows

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items (16)

Random inscribed polytopes in projective geometries ⋮ ON PROJECTIVE EQUIVALENCE AND POINTWISE PROJECTIVE RELATION OF RANDERS METRICS ⋮ Two-dimensional metrics admitting precisely one projective vector field ⋮ On the projective Randers metrics ⋮ Projectively invariant objects and the index of the group of affine transformations in the group of projective transformations ⋮ SPECIAL PROJECTIVE ALGEBRA OF RANDERS METRICS OF CONSTANT S-CURVATURE ⋮ Projective dynamics and first integrals ⋮ Force free projective motions of the sphere ⋮ A solution of a problem of Sophus Lie: normal forms of two-dimensional metrics admitting two projective vector fields ⋮ On the Roter type of Chen ideal submanifolds ⋮ Proof of the projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two ⋮ A class of Finsler metrics admitting first integrals ⋮ Complete Einstein metrics are geodesically rigid ⋮ 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 ⋮ Applications of Nijenhuis geometry II: maximal pencils of multi-Hamiltonian structures of hydrodynamic type ⋮ Lorentzian metrics null-projectively related to semi-Riemannian metrics

Cites Work

• Trajectory equivalence and corresponding integrals
• Projectively equivalent metrics, exact transverse line fields and the geodesic flow on the ellipsoid
• Special symmetric two-tensors, equivalent dynamical systems, cofactor and bi-cofactor systems
• Tensor invariants of natural mechanical systems on compact surfaces, and the corresponding integrals
• Ricci-Calculus

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