This article is cited in 3 papers

Short notes

The Bertrand’s manifolds with equators

E. A. Kudryavtseva, D. A. Fedoseev

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Natural mechanical systems describing the motion of a particle on a two-dimensional Riemannian manifold of revolution in the field of a central smooth potential are studied in the paper. A complete classification of such Riemannian manifolds and potentials on them possessing the strengthened Bertrand property, i.e., any orbit not contained in any meridian is closed, is obtained.

Key words: Bertrand's Riemannian manifold, surface of revolution, equator, Tannery's manifold, the Maupertuis principle.

UDC: 514.853

Received: 24.06.2014

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2016, 71:1, 23–26

Bibliographic databases:

• 
• 
• 
•