arXiv research

Constructs perturbed Fefferman spaces on almost CR manifolds.

An almost Einstein manifold satisfies equations which are a slight weakening of the Einstein equations; Einstein metrics, Poincare-Einstein metrics, and compactifications of certain Ricci-flat asymptotically locally Euclidean structures are special cases. The governing equation is a conformally invariant overdetermined…

We develop a geometric and explicit construction principle that generates classes of Poincare-Einstein manifolds, and more generally almost Einstein manifolds. Almost Einstein manifolds satisfy a generalisation of the Einstein condition; they are Einstein on an open dense subspace and, in general, have a conformal scal…

The study finds limits on dimensions of certain scales and fields for conformal manifolds.

In this article, we study Einstein-Weyl structures on almost cosymplectic manifolds. First we prove that an almost cosymplectic $(κ,μ)$-manifold is Einstein or cosymplectic if it admits a closed Einstein-Weyl structure or two Einstein-Weyl structures. Next for a three dimensional compact almost $α$-cosymplectic manifol…

We study an odd-dimensional analogue of the Goldberg conjecture for compact Einstein almost Kähler manifolds. We give an explicit non-compact example of an Einstein almost cokähler manifold that is not cokähler. We prove that compact Einstein almost cokähler manifolds with non-negative $*$-scalar curvature are cokähler…

The paper investigates $(m,ρ)$-quasi-Einstein structures on almost co-Kähler manifolds.

Study characterizes Einstein manifolds in almost Ricci solitons.

We analyze the classic problem of existence of Einstein metrics in a given conformal structure for the class of conformal structures inducedf Nurowski's construction by (oriented) (2,3,5) distributions. We characterize in two ways such conformal structures that admit an almost Einstein scale: First, they are precisely …

New Einstein metrics found in curved spaces.

It is shown that the first order (Palatini) variational principle for a generic nonlinear metric-affine Lagrangian depending on the (symmetrized) Ricci square invariant leads to an almost-product Einstein structure or to an almost-complex anti-Hermitian Einstein structure on a manifold. It is proved that a real anti-He…

Study second-Chern-Einstein metrics on 4D manifolds, finding Killing vector fields and examples.

In this article, we study almost cosymplectic manifolds admitting quasi-Einstein structures $(g, V, m, λ)$. First we prove that an almost cosymplectic $(κ,μ)$-manifold is locally isomorphic to a Lie group if $(g, V, m, λ)$ is closed and on a compact almost $(κ,μ)$-cosymplectic manifold there do not exist quasi-Einstein…

The paper proves rigidity results for Einstein manifolds with specific geometric constraints.

In this paper, we study the structure of the limit space of a sequence of almost Einstein manifolds, which are generalizations of Einstein manifolds. Roughly speaking, such manifolds are the initial manifolds of some normalized Ricci flows whose scalar curvatures are almost constants over space-time in the $L^1$-sense,…

Study null geodesics on even-dimensional conformal manifolds, finding Einstein metrics and CR structures.

The paper constructs almost para-Kähler-Einstein metrics on cotangent bundles.

Study on solitons in specific geometric manifolds, proving manifold properties and presenting examples.

The paper characterizes gradient solitons in specific manifold types.

The paper presents the Einstein connection for nonsymmetric pseudo-Riemannian manifolds.

On asymptotically complex hyperbolic (ACH) Einstein manifolds, we consider a certain variational problem for almost complex structures compatible with the metric, for which the linearized Euler-Lagrange equation at Kähler-Einstein structures is given by the Dolbeault Laplacian acting on $(0,1)$-forms with values in the…

The paper presents the Einstein connection for nonsymmetric pseudo-Riemannian manifolds with specific torsion conditions.

Study of generalized almost-Kähler-Ricci solitons and their implications.

Eta-Einstein and $(κ,μ)$-structures studied in dimension 3.

The paper studies Einstein-Hilbert action on complex manifolds.

Characterizes when almost smooth spaces become RCD spaces.

The paper characterizes Kenmotsu metrics as almost $*$-Ricci solitons.

New pseudo-Kähler Einstein spaces found with special almost complex structures.

In this paper we introduce the notion of generalized quasi--Einstein manifold, that generalizes the concepts of Ricci soliton, Ricci almost soliton and quasi--Einstein manifolds. We prove that a complete generalized quasi--Einstein manifold with harmonic Weyl tensor and with zero radial Weyl curvature, is locally a war…

In this article, we consider the almost Hermitian structure on $TM$ induced by a pair of a metric and an affine connection on $M$. We find the conditions under which $TM$ admits almost Kähler structures, Kähler structures and Einstein metrics, respectively. Moreover, we give two examples of Kähler-Einstein structures o…

Introduces a restricted Chen-Nagano variational principle for the Einstein-Hilbert functional.

On a 4-dimensional compact symplectic manifold, we consider a smooth family of compatible almost-complex structures such that at time zero the induced metric is Hermite-Einstein almost-Kähler metric with zero or negative Hermitian scalar curvature. We prove, under certain hypothesis, the existence of a smooth family of…

We introduce the notion of Kähler manifolds that are almost Einstein and we define a generalized mean curvature vector field along submanifolds in them. We prove that Lagrangian submanifolds remain Lagrangian, when deformed in direction of the generalized mean curvature vector field. For a Kähler manifold that is almos…

The paper characterizes Einstein metrics in Kenmotsu manifolds using specific soliton types.

Study clarifies almost Ricci-Bourguignon solitons and their properties.

In this article we study almost contact manifolds admitting weakly Einstein metrics. We first prove that if a (2n+1)-dimensional Sasakian manifold admits a weakly Einstein metric then its scalar curvature $s$ satisfies $-6\leqslant s \leqslant 6$ for $n=1$ and $-2n(2n+1)\frac{4n^2-4n+3}{4n^2-4n-1}\leqslant s \leqslant …

Survey updates knowledge on homogeneous Einstein spaces.

It is a well known fact that, if $Σ$ is an Einstein hypersurface with positive scalar curvature, then it is a round sphere. We give a stable version of this result showing that if a hypersurface is almost Einstein in a $L^p$-sense, then it is $W^{2, \, p}$ - close to the round sphere. The result is given in a quantitat…

Unique domain found in Einstein universe, simplifying manifold classification.

This paper is devoted to the first systematic investigation of manifolds that are Einstein for a connection with skew symmetric torsion. We derive the Einstein equation from a variational principle and prove that, for parallel torsion, any Einstein manifold with skew torsion has constant scalar curvature; and if it is …

Conditions for statistical structures on manifolds derived from solitons.

Constructs initial data for Einstein vacuum equations involving multiple localized gravitational sources.

The paper defines a new connection on sub-Riemannian manifolds and explores conditions for almost quasi-Sasakian manifolds to be Einstein.

Einstein like $(\varepsilon)$-para Sasakian manifolds are introduced. For an $(\varepsilon)$-para Sasakian manifold to be Einstein like, a necessary and sufficient condition in terms of its curvature tensor is obtained. The scalar curvature of an Einstein like $(\varepsilon)$-para Sasakian manifold is obtained and it…

Study on para-Sasakian metrics and their solitons.

Study on Ricci solitons and Einstein metrics in weak β-Kenmotsu manifolds.

In this paper, we prove new pinching theorems for the first eigenvalue of the Laplacian on compact hypersurfaces of the Euclidean space. These pinching results are associated with the upper bound for the first eigenvalue in terms of higher order mean curvatures. We show that under a suitable pinching condition, the hyp…

In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almost umbilical hypersurfaces.