Parallel tangency for immersions into Euclidean spaces

摘要

Let M and N be two smoothly immersed manifolds of codimension 2 in the Euclidean space R~(2n). We study the enumerative problem: find the number of the pairs (x, y) ∈ M × N of points so that M_x is parallel to N_y, where M_x(∪) R~(2n)is the tangent space to M at x.