We study the motion of an n-dimensional closed spacelike hypersurface in a Lorentzian manifold in the direction of its past directed normal vector, where the speed equals a positive power p of the mean curvature. We prove that for any p ∈ (0, 1], the flow exists for all time when the Ricci tensor of the ambient space is bounded from below on the set of timelike unit vectors. Moreover, if we ass...

Let s ≥ 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s, s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature homogeneous; their curvature tensor is modeled on that of a local symmetric space. They are spacelike Jordan Osserman with a Jacobi operator which is nilpotent of ord...

0. Introduction A Bézier surface is defined using mathematical spline functions whereby the resulting surface has a compact analytic description. This enables such surfaces to be easily manipulated, and they also have greater continuity properties. Bézier curves and surfaces are commonly used in computer-aided design [1,2], image processing [3,4], and finite elementmodeling (e.g. [5–7]). Many o...