of subsets of TM: Note that i) 8 (p;Xp) 2 TM , as p 2M ) there exists (U ; ) 2 S such that p 2 U ; i.e. (p;Xp) 2 TU , and we have TU = 1 (R) 2 : ii) If we de ne F : TpM ! R by F (Xp) = (Xp(x);… Expand

Properties of submanifolds are examined which remain invariantunder a conformal change of metric of the ambiant space. In particular,the Willmore energy functional is discussed as is the… Expand

1. Let M and M' denote complete riemannian manifolds of dimension n and m respectively, and suppose that M is compact and oriented. For simplicity we assume that both manifolds and their metrics are… Expand