Related papers: On Space-like Class $\mathcal A$ Surfaces in Rober…
We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general…
We introduce several new notions of (sectional) curvature bounds for Lorentzian pre-length spaces: On the one hand, we provide convexity/concavity conditions for the (modified) time separation function, and, on the other hand, we study…
The Robertson-Walker spacetimes are conformally flat and so are conformally invariant under the action of the Lie group SO(4,2), the conformal group of Minkowski spacetime. We find a local coordinate transformation allowing the…
In this note we show that Lorentzian Concircular Structure manifolds (LCS)_n coincide with Generalized Robertson-Walker space-times.
We discuss construction and applications of instanton-like objects which we call fractional space-like branes. These objects are localised at a fixed point of a time-like (or more generally space-time) orbifold which is a string theoretical…
We show that to every maximal surface with conelike singularities in Lorentz-Minkowski space $\mathbb{L}^3$ that can be locally represented as the graph of a smooth function, there exists a corresponding timelike minimal surface in…
This manuscript is devoted to investigate Bianchi Type $I$ universe in the context of $f(R,T)$ gravity. For this purpose, we explore the exact solutions of locally rotationally symmetric Bianchi type $I$ spacetime. The modified field…
In this study, we provide some classifications for half-conformally flat gradient $f$-almost Ricci solitons, denoted by $(M, g, f)$, in both Lorentzian and neutral signature. First, we prove that if $||\nabla f||$ is a non-zero constant,…
This article deals with the investigation of perfect fluid spacetimes endowed with concircular vector field. It is shown that in a perfect fluid spacetime with concircular vector field, the velocity vector field annihilates the conformal…
Let $(M,g)$ be a spacetime. That is, $M$ is a real manifold of dimension $4$ equipped with a Lorentzian metric $g$. We show that any separation of time and space in $M$ is equivalent to introducing a (non-smooth) Riemann metric $h$. If $h$…
For every $g\geq 2$ we distinguish real period matrices of real Riemann surfaces of topological type $(g,0,0)$ from the ones of topological type $(g,k,1)$, with $k$ equal to one or two for $g$ even or odd respectively (Theorem B). To that…
In this article we obtain new rigidity results for spacelike submanifolds of arbitrary codimension in Generalized Robertson-Walker spacetimes. Namely, under appropriate assumptions such as parabolicity we prove by means of some maximum…
In this paper we introduce the notion of timelike surface with harmonic inverse mean curvature in 3-dimensional Lorentzian space forms, and study their fundamental properties.
We determine the local structure of all pseudo-Riemannian manifolds $(M,g)$ in dimensions $n\ge4$ whose Weyl conformal tensor $W$ is parallel and has rank 1 when treated as an operator acting on exterior 2-forms at each point. If one fixes…
We will construct a non-separable Hilbert space for which the inhomogeneous ${\rm SL}(2,\mathbb{C})$ acts on it unitarily. Each vector in this Hilbert space is described by a (rectangular) space-like surface in $\mathbb{R}^4$, for which a…
In this paper, we study the timelike tubular Weingarten surfaces in 3-dimensional Minkowski space $IR_1^3 $.We have obtained some conditions for being $({K_{II},H})$, $({K_{II},K})$, timelike tubular Weingarten surfaces where are the second…
We investigate surfaces with constant harmonic-mean curvature one (HMC-1 surfaces) in hyperbolic three-space. We allow them to have certain kinds of singularities, and discuss some global properties. As well as flat surfaces and surfaces…
In this thesis we define the notion of a locally stratified space. Locally stratified spaces are particular kinds of streams and d-spaces which are locally modelled on stratified spaces. We construct a locally presentable and cartesian…
In (Phys. Rev. D 62, 081501, 2000) we proposed a unified approach to description of continuous and discrete spacetime based on nonassociative geometry and described nonassociative smooth and discrete de Sitter models. In our paper we give…
Observer-invariance is regarded as a minimum requirement for an appropriate definition of time derivatives. We systematically discuss such time derivatives for surface tensor field and provide explicit formulations for material,…