We prove the existence of smooth closed hypersurfaces of prescribed mean curvature homeomorphic to S for small n, n ≤ 6, provided there are barriers. 0. Introduction In a complete (n+1)-dimensional manifold N we want to find closed hypersurfaces M of prescribed mean curvature. To be more precise, let Ω be a connected open subset of N , f ∈ C(Ω̄), then we look for a closed hypersurface M ⊂ Ω such...

We study the semi-Riemannian geometry of foliation F an indefinite locally conformal Kähler (l.c.K.) manifold M, given by Pfaffian equation ω=0, provided that ∇ω=0 and c=∥ω∥≠0 (ω is Lee form M). If M conformally flat then every leaf shown to be a totally geodesic hypersurface in space sectional curvature c/4, carrying c-Sasakian structure. As corollary result together with version de Rham decom...