Chekanov-type theorem for spherized cotangent bundles

Abstract

We prove a Chekanov-type theorem for the spherization of the cotangent bundle $S{T}^{\ast }B$ of a closed manifold $B$. It claims that for Legendrian submanifolds in $S{T}^{\ast }B$ the property "to be given by a generating family quadratic at infinity" persists under Legendrian isotopies.