A novel method is introduced for constructing two-dimensional (2D) surface meshes embedded in three-dimensional (3D) space time and 3D hypersurface four-dimensional (4D) time. In particular, we begin by dividing the space–time domain into slabs. Each slab equipped with an initial plane (hyperplane), conjunction unstructured simplicial (hypersurface) mesh that covers plane. We then obtain vertic...

Four constructions of constant mean curvature (CMC) hypersurfaces in Sn+1 are given, which should be considered analogues of ‘classical’ constructions that are possible for CMC hypersurfaces in Euclidean space. First, Delaunay-like hypersurfaces, consisting roughly of a chain of hyperspheres winding multiple times around an equator, are shown to exist for all the values of the mean curvature. S...

Four constructions of constant mean curvature (CMC) hypersurfaces in S are given, which should be considered analogues of ‘classical’ constructions that are possible for CMC hypersurfaces in Euclidean space. First, Delaunay-like hypersurfaces, consisting roughly of a chain of hyperspheres winding multiple times around an equator, are shown to exist for all values of the mean curvature. Second, ...

In this paper, by the Gauss equation of the induced Chern connection for Finsler submanifolds, we prove that if M is an umbilical hypersurface of a Minkowski space (V , F ), then either M is a Riemannian space form or a locally Minkowski space. AMS subject classifications: 53C60, 53C40

We study di erent notions of blow-up of a scheme X along a subscheme Y , depending on the datum of an embedding of X into an ambient scheme. The two extremes in this theory are the ordinary blow-up, corresponding to the identity, and the `quasi-symmetric blow-up', corresponding to the embedding of X into a nonsingular variety. We prove that this latter blow-up is intrinsic of Y and X , and is u...

We study the issue of description spinning particle dynamics by means recently proposed world sheet concept. A model irreducible in 3d Minkowski space with two gauge symmetries is considered. The classical trajectories free lie on a circular cylinder time-like axis. direction axis determined momentum, and its position space-time depends value total angular momentum. radius representation. admit...