We study the Nehari manifold N associated to the boundary value problem −∆u = f(u) , u ∈ H 0 (Ω) , where Ω is a bounded regular domain in Rn. Using elementary tools from Differential Geometry, we provide a local description of N as an hypersurface of the Sobolev space H1 0 (Ω). We prove that, at any point u ∈ N , there exists an exterior tangent sphere whose curvature is the limit of the increasing sequence of principal curvatures of N . Also, the H1-norm of u ∈ N depends on the number of principal negative curvatures. Finally, we study basic properties of an angle decreasing flow on the Nehari manifold associated to homogeneous non–linearities. MSC: 35J15, 35J25, 35J50, 53A07 .