arXiv research

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

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…

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

Study new Einstein-like metrics and their properties.

The paper characterizes gradient solitons in specific manifold types.

The study provides volume growth estimates for specific types of manifolds.

We present a general numerical method for investigating prescribed Ricci curvature problems on toric Kähler manifolds. This method is applied to two generalisations of Einstein metrics, namely Ricci solitons and quasi-Einstein metrics. We begin by recovering the Koiso--Cao soliton and the Lü--Page--Pope quasi-Einstein …

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

The study characterizes GRW spacetimes with gradient solitons and phantom era.

This paper proves certain quasi-Einstein manifolds are rigid under Ricci flow.

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

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 characterizes spacetimes with specific solitons in $f(\mathcal{R})$-gravity.

We construct quasi-Einstein metrics on some hypersurface families. The hypersurfaces are circle bundles over the product of Fano, Kähler-Einstein manifolds. The quasi-Einstein metrics are related to various gradient Kähler-Ricci solitons constructed by Dancer and Wang and some Hermitian, non-Kähler, Einstein metrics co…

We call a metric quasi-Einstein if the $m$-Bakry-Emery Ricci tensor is a constant multiple of the metric tensor. This is a generalization of Einstein metrics, which contains gradient Ricci solitons and is also closely related to the construction of the warped product Einstein metrics. We study properties of quasi-Einst…

The study explores $(m,ρ)$-quasi-Einstein structures on contact metric manifolds.

The notion of quasi-Einstein metric in physics is equivalent to the notion of Ricci soliton in Riemannian spaces. Quasi-Einstein metrics serve also as solution to the Ricci flow equation. Here, the Riemannian metric is replaced by a Hessian matrix derived from a Finsler structure and a quasi-Einstein Finsler metric is …

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 …

The differential geometry of Kenmotsu manifold is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In fact, its statistical counterpart, that is, Kenmotsu statistical manifold also has same importance as that of Kenmotsu manifold. Theoretical physicists have also b…

Study geometric properties and physical applications of mixed quasi-Einstein spacetime.

Study rigidifies non-compact manifolds with specific curvature conditions.

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.

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…

In this paper we introduce the notion of Einstein-type structure on a Riemannian manifold $\varrg$, unifying various particular cases recently studied in the literature, such as gradient Ricci solitons, Yamabe solitons and quasi-Einstein manifolds. We show that these general structures can be locally classified when th…

Study on compact Quasi-Einstein manifolds yields diameter estimates and Hitchin-Thorpe inequality conditions.

Study on rigidity of special Riemannian manifolds.

We call a metric $m$-quasi-Einstein if $Ric_X^m$ (a modification of the $m$-Bakry-Emery Ricci tensor in terms of a suitable vector field $X$) is a constant multiple of the metric tensor. It is a generalization of Einstein metrics which contains Ricci solitons. In this paper, we focus on left-invariant vector fields and…

We call a metric $m$-quasi-Einstein if $Ric_X^m$, which replaces a gradient of a smooth function $f$ by a vector field $X$ in $m$-Bakry-Emery Ricci tensor, is a constant multiple of the metric tensor. It is a generalization of Einstein metrics which contains Ricci solitons. In this paper, we focus on left-invariant met…

This paper studies cohomogeneity one Ricci solitons. If the isotropy representation of the principal orbit $G/K$ consists of two inequivalent $Ad_K$-invariant irreducible summands, the existence of parameter families of non-homothetic complete steady and expanding Ricci solitons on non-trivial bundles is shown. These e…

In the context of paracontact geometry, $η$-Ricci solitons are considered on manifolds satisfying certain curvature conditions: $(ξ,\cdot)_{R}\cdot S=0$, $(ξ,\cdot)_{S}\cdot R=0$, $(ξ,\cdot)_{W_2}\cdot S=0$ and $(ξ,\cdot)_{S}\cdot W_2=0$. We prove that on a para-Kenmotsu manifold $(M,\varphi,ξ,η,g)$, the existence of a…

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…

We numerically calculate Perelman's entropy for a variety of canonical metrics on $\mathbb{CP}^{1}$-bundles over products of Fano Kähler-Einstein manifolds. The metrics investigated are Einstein metrics, Kähler-Ricci solitons and quasi-Einstein metrics. The calculation of the entropy allows a rough picture of how the R…

The paper proves the existence of Sasaki-Einstein metrics on specific Sasakian manifolds.

Paper confirms Hamilton-Tian conjecture for specific Sasakian manifolds.

The linear stability of warped product Einstein metrics as fixed points of the Ricci flow is investigated. We generalise the results of Gibbons, Hartnoll and Pope and show that in sufficiently low dimensions, all warped product Einstein metrics are unstable. By exploiting the relationship between warped product Einstei…

The study examines perfect fluid spacetimes and their properties.

Exposes new connections between weighted Kähler-Ricci solitons and Ricci-flat Kähler cone metrics.

This paper classifies solitons under specific tensor conditions.

Study weak $f$-K-contact manifolds, finding Einstein-type metrics and solitons.

The study investigates properties of a specific Riemannian manifold with a semi-symmetric non-metric connection.

The study characterizes quasi Yamabe solitons with potential vector fields.

Paper shows constant σk-curvature for quasi k-Yamabe solitons.

The study classifies specific types of solitons with bounded scalar curvature.

Using the tractor calculus to study smooth metric measure spaces, we adapt results of Gover and Nurowski to give sharp metric obstructions to the existence of quasi-Einstein metrics on suitably generic manifolds. We do this by introducing an analogue of the Weyl tractor $W$ to the setting of smooth metric measure space…

The paper examines geometric properties of a specific black hole spacetime.

We prove that a nontrivial complete generalized quasi Yamabe gradient soliton (M; g) must be a quasi Yamabe gradient soliton on each connected component of M and that a nontrivial complete locally conformally at generalized quasi Yamabe gradient soliton has a special warped product structure.

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

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