Topology of Certain Closed Submanifolds in Euclidean Space

Recently P.F,Leung has investigated the topological characters of certaincompact oriented submanifolds minimally immersed in the unit sphere S~(n+p).It iswell known that a immersed submanifold in S~(n+p) can be always regarded as a sub-manifold in n+p+1-dimensional Euclidean space R~(n+p+1) and there is no minimalclosed submanifold in R~(n+p+1).Thus,it is a natural and important problem tostudy the topological properties of general closed submanifolds in R~N. Through