相关论文: The Friedmann-Lemaitre models in perspective

We revisit the Riemann-Cartan geometry in the context of recent higher-dimensional theories of spacetime. After introducing the concept of torsion in a modern geometrical language we present some results that represent extensions of…

In their proof of the positive energy theorem, Schoen and Yau showed that every asymptotically flat spacelike hypersurface M of a Lorentzian manifold which is flat along M can be isometrically imbedded with its given second fundamental form…

A well-known theorem of Assouad states that metric spaces satisfying the doubling property can be snowflaked and bi-Lipschitz embedded into Euclidean spaces. Due to the invariance of many geometric properties under bi-Lipschitz maps, this…

We give a new proof of the generalized Minkowski identities relating the higher degree mean curvatures of orientable closed hypersurfaces immersed in a given constant sectional curvature manifold. Our methods rely on a fundamental…

In this paper, we investigate pure geometric $f(R)$ cosmology branes embedded in five-dimensional spacetime. The form of $f(R)$ is chosen as a polynomial. The Five-dimensional scalar curvature $R$ is assumed to be constant. Based on the…

The formulas for the 3-dimensional distance and the velocity modulus in the 4-dimensional linear space with the Berwald-Moor metrics are obtained. The used algorithm is applicable both for the Minkowski space and for the arbitrary…

Procedure of constructing the BPS solutions in SO(3) model on the background of 4D-space-time with the spatial part as a model of constant curvature: Euclid, Riemann, Lobachevsky, is reexamined. It is shown that among possible…

Due to Janet-Cartan's theorem, any analytic Riemannian manifolds can be locally isometrically embedded into a sufficiently high dimensional Euclidean space. However, for an individual Riemannian manifold (M,g), it is in general hard to…

A criticism sometimes made of the causal set quantum gravity program is that there is no practical scheme for identifying manifoldlike causal sets and finding embeddings of them into manifolds. A computational method for constructing an…

We study Sobolev spaces of radial functions on spherically symmetric Riemannian manifolds. Using geodesic polar coordinates, we give a sharp one-dimensional reduction: a radial function belongs to the Sobolev space on the manifold if and…

This essay summarizes the efforts required to build a program of a unified, low-dimension topology that allows characterizing all these flat space-times. Since spatiotemporal manifolds are topological spaces equipped with metrics, their…

A {\it wrinkled embedding} $f:V^n\to W^m$ is a topological embedding which is a smooth embedding everywhere on $V$ except a set of $(n-1)$-dimensional spheres, where $f$ has cuspidal corners. In this paper we prove that any rotation of the…

We obtain higher dimensional analogues of the results of Mantoulidis and Schoen in [8]. More precisely, we show that (i) any metric $g$ with positive scalar curvature on the $3$-sphere $S^3$ can be realized as the induced metric on the…

We consider a concircularly semi-symmetric metric connection and its application. The Ricci tensors with respect to the concircularly semi-symmetric metric connection are symmetric, and they are used to define Einstein type manifolds. In…

In this work, we study various properties of embedded hypersurfaces in $1+1+2$ decomposed spacetimes with a preferred spatial direction, denoted $e^{\mu}$, which are orthogonal to the fluid flow velocity of the spacetime and admit a proper…

Computing correlation functions in curved spacetime is central to both theoretical and experimental efforts, from precision cosmology to quantum simulations of strongly coupled systems. In anti-de Sitter (AdS) and de Sitter (dS) space, the…

We present a global metric describing closed timelike curves embedded in Minkowski spacetime. Physically, the metric represents an Alcubierre warp drive on a rotating platform. The physical realizability of such a metric is uncertain due to…

The space of embedded submanifolds plays an important role in applications such as computational anatomy and shape analysis. We can define two different classes on Riemannian metrics on this space: so-called outer metrics are metrics that…

Considering the scale dependent effective spacetimes implied by the functional renormalization group in d-dimensional Quantum Einstein Gravity, we discuss the representation of entire evolution histories by means of a single, (d +…

We derive total mean curvature integration formulae of a three co-dimensional foliation $\mathcal{F}^{n}$ on a screen integrable half-lightlike submanifold, $M^{n+1}$ in a semi-Riemannian manifold $\overline{M}^{n+3}$. We give generalized…