On Riemannian manifolds satisfying a certain curvature condition imposed on the Weyl curvature tensor
In this paper we present a review of recent results on semi-Riemannian manifolds satisfying curvature conditions of pseudosymmetry type.
We investigate the geometry at infinity of the so-called “gravitational instantons”, i.e. asymptotically flat hyperkähler four-manifolds, in relation with their volume growth. In particular, we prove that gravitational instantons with cubic volume growth are ALF, namely asymptotic to a circle fibration over a Euclidean three-space, with fibers of asymptotically constant length.
In a crystalline algorithm, a tangential velocity is used implicitly. In this short note, it is specified for the case of evolving plane curves, and is characterized by using the intrinsic heat equation.
We study the existence of surfaces with constant or prescribed Gauss curvature in certain Lorentzian spacetimes. We prove in particular that every (non-elementary) 3-dimensional maximal globally hyperbolic spatially compact spacetime with constant non-negative curvature is foliated by compact spacelike surfaces with constant Gauss curvature. In the constant negative curvature case, such a foliation exists outside the convex core. The existence of these foliations, together with a theorem of C. Gerhardt,...