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Feb 3, 2013 at 0:44 comment added aglearner Mohan, this is interesting. I wonder if you need $n\le N+2$, so that through a generic point at least one-dimensional family of lines passes, which would imply (if full non-integrability of this distribution is established) that any two points on the hypersuface can be joined by a chain of lines? Anyway, I don't know how to make this rigorous, I and am curious to know how you would prove your claim.
Feb 2, 2013 at 20:49 history answered Mohan CC BY-SA 3.0