Hi everyone, a couple of technical questions : 1) Definition: Anyone know the definition of the induced orientation of a submanifold S of an orientable manifold M? 2)Dividing sets in contact manifolds: We have a contact 3-manifold (M3,ζ ). We define a surface S embedded in M3 to be a convex surface if there exists a contact vector field X that is transverse to S, i.e., X does not live on the surface; X is not in the span of any basis for TpS. Now, we define the dividing set of the surface S to be the set of points of X that live in the contact planes , i.e., p is in the dividing set if X(p) is in ζ(p) ; ζ(p) is the contact plane at the point p, and X(p) is the contact vector field at p ( a contact vector field for (M3,ζ ) is a vector field whose flow preserves ζ , i.e., LXζ=gζ , where L is the Lie derivative of the form ζ along the vector field X, and g is a positive smooth function. So, say I have the standard contact structure in R3 given by ker(cos(πr)dx+sin(πr)dθ) . I know ∂/∂z is a contact field , so that it is transverse to any disk in the xy-plane. How do I find the dividing set in this case? I need to find the points in R3 so that ∂/∂z (p) ( basically, the z-axis "based at p " ) lies in the contact plane at p. I'm kind of stuck in a loop here; any suggestions, please ? Thanks.