In the standard contact (2n + 1)-space when n > 1, we construct infinite families of pairwise non-Legendrian isotopic, Legendrian n-spheres, n-tori and surfaces which are indistinguishable using classically known invariants. When n is even, these are the first known examples of non-Legendrian isotopic, Legendrian submanifolds of (2n + 1)-space. Such constructions indicate a rich theory of Legendrian submanifolds. To distinguish our examples, we compute their contact homology which was rigorously defined in this situation in .
"Non-isotopic Legendrian submanifolds in R2n+1." J. Differential Geom. 71 (1) 85 - 128, September 2005. https://doi.org/10.4310/jdg/1143644313