arXiv research

Study properties of Kenmotsu manifolds with conformal η-Einstein soliton metrics.

Study properties of para-Kähler manifolds with conformal Einstein soliton metrics.

The paper studies special solitons on specific contact metric manifolds.

Study on para-Sasakian metrics and their solitons.

The paper characterizes Kenmotsu manifolds with conformal η-Ricci solitons.

The paper examines conditions for conformal Ricci solitons on generalized ($κ, μ$)-space forms.

In this paper we extend some well-known rigidity results for conformal changes of Einstein metrics to the class of generalized quasi-Einstein (GQE) metrics, which includes gradient Ricci solitons. In order to do so, we introduce the notions of conformal diffeomorphisms and vector fields that preserve a GQE structure. W…

The paper explores $*$-conformal $η$-Ricci solitons in Kenmotsu manifolds.

Study on Ricci-Bourguignon solitons on specific product spaces.

The paper characterizes Clairaut conformal submersions on Ricci solitons.

We construct examples of Bach-flat gradient Ricci solitons which are neither half conformally flat nor conformally Einstein.

In this paper we introduce, in the Riemannian setting, the notion of conformal Ricci soliton, which includes as particular cases Einstein manifolds, conformal Einstein manifolds and (generic and gradient) Ricci solitons. We provide here some necessary integrability conditions for the existence of these structures that …

We investigate Kähler metrics conformal to gradient Ricci solitons, and base metrics of warped product gradient Ricci solitons. The latter we name quasi-solitons. A main assumption that is employed is functional dependence of the soliton potential, with the conformal factor in the first case, and with the warping funct…

The study classifies gradient Ricci solitons with specific vector fields.

Study on gradient ρ-Einstein solitons with radially nonnegative Bach tensor.

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…

This paper classifies Kähler manifolds with specific Einstein-type properties.

New families of Ricci solitons found with collapsing volume.

The study characterizes mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons.

The paper examines gradient ρ-Einstein solitons on specific manifolds and spacetimes.

The main purpose of the paper is to prove that if a compact Riemannian manifold admits a gradient $ρ$-Einstein soliton such that the gradient Einstein potential is a non-trivial conformal vector field, then the manifold is isometric to the Euclidean sphere. We have showed that a Riemannian manifold satisfying gradient …

Study on $ρ$-Einstein solitons with zero scalar curvature, proving stability and flatness.

The local structure of half conformally flat gradient Ricci almost solitons is investigated, showing that they are locally conformally flat in a neighborhood of any point where the gradient of the potential function is non-null. In opposition, if the gradient of the potential function is null, then the soliton is a ste…

Axisymmetric Ricci solitons are rigid under non-axisymmetric perturbations.

In this paper, we classify n-dimensional (n>3) complete Bach-flat gradient shrinking Ricci solitons. More precisely, we prove that any 4-dimensional Bach-flat gradient shrinking Ricci soliton is either Einstein, or locally conformally flat hence a finite quotient of the Gaussian shrinking soliton $R^4$ or the round cyl…

In this paper we prove that any complete locally conformally flat quasi-Einstein manifold of dimension $n\geq 3$ is locally a warped product with $(n-1)$-dimensional fibers of constant curvature. This result includes also the case of locally conformally flat gradient Ricci solitons.

The paper explores conformal submersions from Ricci solitons to Riemannian manifolds.

The paper solves gradient Schouten solitons on specific geometric structures.

In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant $\varphi$-sectional curvature, and prove the structure theorem for $ξ$-conformally fla…

This paper classifies solitons under specific tensor conditions.

The study examines perfect fluid spacetimes and their properties.

Study proves structure results for homogeneous spaces supporting specific equations.

The study examines curvature tensors and solitons in Lorentzian trans-Sasakian space forms.

Study on Ricci solitons on tangent and unit tangent bundles.

On an $n$-dimensional complete manifold $M$, consider an $h$-almost gradient Ricci soliton, which is a generalization of a gradient Ricci soliton. We prove that if the manifold is Bach-flat and $dh/du>0$, then the manifold $M$ is either Einstein or rigid. In particular, such a manifold has harmonic Weyl curvature. More…

English translation of "Solitony Ricciego" (Wiadomości Matematyczne 48, 2012, no. 1, pp. 1-32). Despite the general-sounding title, the text covers just a few narrow topics: Perelman's proof of the fact that compact Ricci solitons are of the gradient type, and a detailed unified description of Page's and Berard Bergery…

We study locally conformal calibrated $G_2$-structures whose underlying Riemannian metric is Einstein, showing that in the compact case the scalar curvature cannot be positive. As a consequence, a compact homogeneous $7$-manifold cannot admit an invariant Einstein locally conformal calibrated $G_2$-structure unless the…

In this paper we consider $M = B\times_{f}F$ warped product gradient Ricci solitons. We proved that the potential function depends only on the base and the fiber $F$ is necessarily Einstein manifold. We provide all such solutions in the case of steady gradient Ricci solitons when the base is conformal to an $n$-dimensi…

Study Clairaut maps on Kähler manifolds with Ricci solitons, finding curvature and scalar relations.

We study a characterization of 4-dimensional (not necessarily complete) gradient Ricci solitons $(M, g, f)$ which have harmonic Weyl curvature, i.e. $δW=0$. Roughly speaking, we prove that the soliton metric $g$ is locally isometric to one of the following four types: an Einstein metric, the product $ \mathbb{R}^2 \tim…

Smooth metric measure spaces have been studied from the two different perspectives of Bakry-Émery and Chang-Gursky-Yang, both of which are closely related to work of Perelman on the Ricci flow. These perspectives include a generalization of the Ricci curvature and the associated quasi-Einstein metrics, which include Ei…

The paper studies extended quasi-Einstein manifolds with special geometric properties and solitons.

Let $M$ be a compact complex manifold admitting a Kähler structure. A conformally Kähler, Einstein-Maxwell metric (cKEM metric for short) is a Hermitian metric $\tilde{g}$ on $M$ with constant scalar curvature such that there is a positive smooth function $f$ with $g = f^2 \tilde{g}$ being a Kähler metric and $f$ being…

Study explores geometric properties of Vaidya-Bonner-de Sitter spacetime.

Study on 3D trans-Sasakian manifolds with η-Einstein solitons.

Compact gradient ρ-Einstein solitons are isometric to Euclidean spheres.

Study on Einstein solitons with bounds and asymptotic behavior.

The paper investigates geometrical aspects of static spacetime with almost gradient Ricci solitons.