arXiv research

Detect spacetime curvature with event causality measurements.

In this work we study Berwald spacetimes and their vacuum dynamics, where the latter are based on a Finsler generalization of the Einstein's equations derived from an action on the unit tangent bundle. In particular, we consider a specific class of spacetimes which are non-flat generalizations of the very special relat…

New findings on plane waves in 3D spacetimes, showing non-unimodular elliptic plane waves are unique.

We show that timelike maximal cylinders in $\RR^{1 + 2}$ always develop singularities in finite time and that, infinitesimally at a generic singularity, their time slices are evolved by a rigid motion or a self-similar motion. We also prove a mild generalization in non-flat backgrounds.

Mathematical treatment of plane waves, proving their inextendibility and completeness.

The paper classifies PMCV hypersurfaces in non-flat pseudo-Riemannian space forms.

The paper constructs a new Ricci-flat metric on almost abelian Lie groups.

We classify pseudo parallel proper CR-submanifolds in a non-flat complex space form with CR-dimension greater than one. With this result, the non-existence of recurrent as well as semi parallel proper CR-submanifolds in a non-flat complex space form with CR-dimension greater than one can also be obtained.

A purely algebraic construction of super-energy tensors for arbitrary fields is presented in any dimensions. These tensors have good mathematical and physical properties, and they can be used in any theory having as basic arena an n-dimensional manifold with a metric of Lorentzian signature. In general, the completely …

In this paper, we show that there exists no equifocal submanifold with non-flat section in four irreducible simply connected symmetric spaces of compact type and rank two. Also, we show a fact for the sections of equifocal submanifolds with non-flat section in other irreducible simply connected symmetric spaces of comp…

In this paper, I prove a splitting theorem for equifocal submanifolds with non-flat section in a simply connected symmetric space of compact type. Also, by using the splitting theorem, I prove that the sections of equifocal submanifolds with non-flat section in an irreducible simply connected symmetric space of compact…

In this paper the result of real hypersurfaces in non-flat complex space forms, whose structure vector field $ξ$ belongs to the $κ$-nullity distribution is extended in case of three dimensional real hypersurfaces in non-flat complex space forms. Furthermore, generalization of notion ($κ$,$μ$)-nullity distribution defin…

It has been proved that there are no real hypersurfaces satisfying RA = 0 in non-flat complex space forms. In this paper we prove that the same is true in the case of CR submanifolds of maximal CR dimension, that is there are no CR submanifolds of maximal CR dimension satisfying RA = 0 in non-flat complex space forms.

We construct a series of examples of non--flat non--homogeneous parabolic geometries that carry a symmetry of the parabolic geometry at each point.

Taubes proved that all compact oriented four-manifolds admit non-flat instantons. We show that there exists a non-compact oriented four-manifold having no non-flat instanton.

Kaimakamis and Panagiotidou in \cite{KP} introduced the notion of $^*$-Ricci soliton and studied the real hypersurfaces of a non-flat complex space form admitting a $^*$-Ricci soliton whose potential vector field is the structure vector field. In this article, we consider that a real hypersurface of a non-flat complex …

Constructs integrable hierarchies for generalized Frobenius manifolds with non-flat unity.

Study finds formulas for special curves in complex spaces.

This paper focuses on the study of three dimensional real hypersurfaces in non-flat complex space forms whose $^{*}$-Ricci tensor satisfies conditions of parallelism. More precisely, extension of existing results concerning real hypersurfaces with vanishing, semi-parallel and pseudo-parallel $^{*}$-Ricci tensor in case…

In this paper, by studying the position of umbilical normal vectors in the normal bundle, we prove that pseudo-umbilical totally real submanifolds with flat normal connection in non-flat complex space forms must be minimal.

Study on non-flat two-plectic geometry of six-sphere and its Hamiltonian dynamics.

We establish an inequality among the Ricci curvature, the squared mean curvature, and the normal curvature for real hypersurfaces in complex space forms. We classify real hypersurfaces in two-dimensional non-flat complex space forms which admit a unit vector field satisfying identically the equality case of the inequal…

We show that for any solvable Lie group of real type, any homogeneous Ricci flow solution converges in Cheeger-Gromov topology to a unique non-flat solvsoliton, which is independent of the initial left-invariant metric. As an application, we obtain results on the isometry groups of non-flat solvsoliton metrics and Eins…

We establish 2-jet determinacy for the symmetry algebra of the underlying structure of any (complex or real) parabolic geometry. At non-flat points, we prove that the symmetry algebra is in fact 1-jet determined. Moreover, we prove 1-jet determinacy at any point for a variety of non-flat parabolic geometries - in parti…

In this paper we consider non-compact non-flat simply connected harmonic manifolds. In particular, we show that the Martin boundary and Busemann boundary coincide for such manifolds. For any finite volume quotient we show that (up to scaling) there is a unique Patterson-Sullivan measure and this measure coincides with …

Classifies symmetries of non-flat 3-webs around a point.

Based on a well-known fact that there are no Einstein hypersurfaces in a non-flat complex space form, in this article we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hyersurface of a non-flat complex space form. For the real hypersurface with quasi-Einstein metric of …

Anomaly flow studied on flat and non-flat nilmanifolds.

New Einstein solvmanifolds created from non-flat Ricci solitons.

New proof shows no equifocal submanifolds with non-flat sections in certain symmetric spaces.

We prove a sharp lower bound on the curvatures of non-flat ASD connections over the cylinder.

We construct new explicit compact supersymmetric valid solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic equations of motion in dimension six. We present balanced Hermitian structures on compact nilmanifolds in dimension six satisfying the heterotic supersymmetry equations…

Post-Lie algebra structure found on non-flat manifolds with curvature and torsion.

The paper classifies path structures on 3D Lie groups and reduces non-flat ones to Z/2Z-structures.

The aim of the present paper is the study of real hypersurfaces equipped with the condition $φl = l φ$, $l = R(., ξ, ξ)$.

Some aspects of Dirac spinors are resumed and studied in order to interpret mathematically the P and T operations in a gravitational field.

We show that an indefinite Euclidean complex space is not a relative of an indefinite non-flat complex space form. We further study whether two compact Fubini-Study spaces are relatives or not.

New homogeneous manifolds with invariant Bismut Ricci flat connections are constructed.

The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.

Constructs Cartan geometries from automorphism behaviors.

The aim of the present paper is the study of some classes of real hypersurfaces equipped with the condition φl = l φ, (l = R(., ξ, ξ))

We consider (flat) Cauchy-complete GH spacetimes, i.e., globally hyperbolic flat lorentzian manifolds admitting some Cauchy hypersurface on which the ambient lorentzian metric restricts as a complete riemannian metric. We define a family of such spacetimes - model spacetimes - including four subfamilies: translation sp…

The paper classifies special geometric shapes in 2D and 3D.

Jebsen-Birkhoff theorem extended to Berwald spacetimes.

The paper introduces and analyzes pseudo generalized Ricci-recurrent spacetimes in modified gravity.

This paper defines directional derivatives and solves Maxwell's equations in curved 3D space.

The study characterizes spacetimes with quasi-constant sectional curvature and explores their properties in $\mathcal{F}(\mathcal{R})$-gravity.

The article introduces pseudo generalized Ricci-recurrent spacetimes and their applications in modified gravity.