Abstract:

In this paper,we introcduce a real projective algebeaic manifold which is the product manifold p^m\times p^q embeds into pⁿ,
n=(m+1)(q+1)-1, where pm,pq and pn are all the real projective space with m, q and n dimension respectively.This embeding submanifold in pⁿ has a foliation with codimension q, all of its leaves are compact.