Related papers: Premanifolds

We study the topology of the space $\d\K^n$ of complete convex hypersurfaces of $\R^n$ which are homeomorphic to $\R^{n-1}$. In particular, using Minkowski sums, we construct a deformation retraction of $\d\K^n$ onto the Grassmannian space…

In this paper, we study the Dirichlet problem for a class of prescribed curvature equations in Minkowski space. We prove the existence of smooth spacelike hypersurfaces with a class of prescribed curvature and general boundary data based on…

We consider $n+1$ dimensional smooth Riemannian and Lorentzian spaces satisfying Einstein's equations. The base manifold is assumed to be smoothly foliated by a one-parameter family of hypersurfaces. In both cases---likewise it is usually…

In this paper, we study locally strongly convex affine hyperspheres in the unimodular affine space $\mathbb{R}^{n+1}$ which, as Riemannian manifolds, are locally isometric to the Riemannian product of two Riemannian manifolds both…

A common approach to metric-affine, local Poincar\'e, special-relativistic and Galilei spacetime geometry is developed. Starting from an affine composite bundle, we introduce local reference frames and their evolution along worldlines and…

We extend the notion of super-Minkowski space-time to include $\mathbb{Z}_2^n$-graded (Majorana) spinor coordinates. Our choice of the grading leads to spinor coordinates that are nilpotent but commute amongst themselves. The mathematical…

In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is…

We argue for more widespread use of manifold-like polyfolds (M-polyfolds) as differential geometric objects. M-polyfolds possess a distinct advantage over differentiable manifolds, enabling a smooth and local change of dimension. To…

We construct examples of complete Riemannian manifolds having the property that every geodesic lies in a totally geodesic hyperbolic plane. Despite the abundance of totally geodesic hyperbolic planes, these examples are not locally…

We study biharmonic hypersurfaces in a generic Riemannian manifold. We first derive an invariant equation for such hypersurfaces generalizing the biharmonic hypersurface equation in space forms studied in \cite{Ji2}, \cite{CH}, \cite{CMO1},…

This set of lectures contain a brief review of some basic supersymmetry and its representations, with emphasis on superspace and superfields. Starting from the Poincar\'e group, the supersymmetric extensions allowed by the Coleman-Mandula…

We investigate a variational problem in the Lorentz-Minkowski space $\l^3$ whose critical points are spacelike surfaces with constant mean curvature and making constant contact angle with a given support surface along its common boundary.…

Consider a complete Riemannian manifold $M^n$ and let $\Sigma^n$ be an orientable hypersurface of the product manifold $M\times\mathbb{R}$ endowed with its standard product metric $\langle \,,\, \rangle.$ Let $\nabla\xi$ denote the gradient…

In the Minkowski space-time, a world hyper-sheet is a timelike hypersurface consisting of a one-parameter family of spacelike submanifolds. Recently, Bousso and Randall introduced the notion of caustics of world hyper-sheets in order to…

This survey is an introduction to the geometry of co-Minkowksi space, the space of unoriented spacelike hyperplanes of the Minkowski space. Affine deformations of cocompact lattices of hyperbolic isometries act on it, in a way similar to…

We establish the linear instability of the semiclassical Einstein-Klein-Gordon system linearised about the Minkowski vacuum spacetime. The proof relies on formulating a forcing problem for both metric and state perturbations within the…

This paper deals with the generalization of usual round spheres in the flat Minkowski spacetime to the case of a generic four-dimensional spacetime manifold $M$. We consider geometric properties of sphere-like submanifolds in $M$ and…

In this article, we first establish the main tool - an integral formula for Riemannian manifolds with multiple boundary components (or without boundary). This formula generalizes Reilly's original formula from \cite{Re2} and the recent…

In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e. a space endowed with a (in general non-diagonal) metric tensor, whose coefficients do depend on a set of non-metrical…

A minimal space-like surface in Minkowski space-time is said to be of general type if it is free of degenerate points. The fact that minimal space-like surfaces of general type in Minkowski space-time admit canonical parameters of the first…