Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4605810 | Differential Geometry and its Applications | 2016 | 10 Pages |
Abstract
Consider the standard symplectic (R2n,Ï0), a point pâR2n and an immersed closed orientable hypersurface ΣâR2nâ{p}, all in general position. We study the following passage/tangency question: how many lines in R2n pass through p and tangent to Σ parallel to the 1-dimensional characteristic distribution kerâ¡(Ï0|TΣ)âTΣ of Ï0. We count each such line with a certain sign, and present an explicit formula for their algebraic number. This number is invariant under regular homotopies in the class of a general position of the pair (p,Σ), but jumps (in a well-controlled way) when during a homotopy we pass a certain singular discriminant. It provides a low bound to the actual number of these isotropic lines.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Sergei Lanzat,