1997/10/13 by Petr E. Pushkar, Pushkar, Petr E. · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #Elasticity and Wave Propagation #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.math/9710219
openalex publication_date 1997/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Chekanov theorem generalizes the classic Lyusternik-Shnirel'man and Morse theorems concerning critical points of a smooth function on a closed manifold. A Legendrian submanifold Λof space of 1-jets of the functions on a manifold M defines a multi-valued function whose graph is the projection of Λin J0 M = M x R. The Chekanov theorem asserts that if Λis homotopic to the 1-jet of a smooth function in the class of embedded Legendrian manifolds, then such a graph of a multi-valued function must have a lot of points (their number is determined by the topology of M) at which the tangent plane to the graph is parallel to M × 0. In the present paper a similar estimate is proved for a wider class of Legendrian manifolds. We consider Legendrian manifolds homotopic (in the class of embedded Legendrian manifolds) to Legendrian manifolds specified by generating families.