arXiv research

Study finds all conformal Ricci collineations on specific 3D Lorentzian groups.

The study examines Ricci solitons and curvature inheritance on Robinson-Trautman spacetimes.

The paper examines geometric properties of a unique spacetime model.

Conditions for Riemannian manifolds to be Euclidean spheres or spaces.

Classifies Ricci collineations on specific 3D Lorentzian Lie groups.

Study finds all Ricci collineations for specific connections on 3D Lorentzian groups.

The study classifies special flows on specific geometric groups.

The purpose of the present article is to study and characterize sev- eral types of symmetries of generalized Robertson-Walker space-times. Con- formal vector fields, curvature and Ricci collineations are studied. Many im- plications for existence of these symmetries on generalied Robertson-Walker spacetimes are obtaine…

Locally homogeneous Lorentzian three-manifolds with recurrect curvature are special examples of Walker manifolds, that is, they admit a parallel null vector field. We obtain a full classification of the symmetries of these spaces, with particular regard to symmetries related to their curvature: Ricci and matter colline…

Solves non-Archimedean Calabi-Yau equation on complex log pairs.

The Ricci Calabi functional is a functional on the space of Kähler metrics of Fano manifolds. Its critical points are called generalized Kähler Einstein metrics. In this article, we show that the Hessian of the Ricci Calabi functional is non-negative at generalized Kähler Einstein metrics. As its application, we give a…

Survey of geometric flows from unified string theories.

We consider the three-dimensional Heisenberg group, equipped with any left-invariant metric, either Lorentzian or Riemannian. We completely classify their affine vector fields and investigate their relationship with Killing vector fields and their casual character. We also classify their Ricci, curvature and matter col…

Generalizes Collins' theorem to products of locally indicable groups.

Considering prolongation of a Lie algebroid equipped with a spray, defining some classical tensors, we show that a Lie symmetry of a spray is a curvature collineation for these tensors.

The paper studies conformal Ricci solitons in warped product spaces.

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

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

Let $F$ be Cayley's ruled cubic surface in a projective three-space over any commutative field $K$. We determine all collineations fixing $F$, as a set, and all cubic forms defining $F$. For both problems the cases $|K|=2,3$ turn out to be exceptional. On the other hand, if $|K|\geq 4$ then the set of simple points of …

The paper characterizes Clairaut conformal submersions on Ricci solitons.

In this note we study conformal Ricci flow introduced by Arthur Fischer. We use DeTurck's trick to rewrite conformal Ricci flow as a strong parabolic-elliptic partial differential equations. Then we prove short time existences for conformal Ricci flow on compact manifolds as well as on asymptotically flat manifolds. We…

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

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

Plasma toroidal metric singularities in helical devices and tokamaks, giving rise to magnetic surfaces inside the plasma devices are investigated in two cases. In the first we consider the case of a rotational plasma on an helical device with circular cross-section and dissipation. In this case singularities are shown …

In this paper we study *-Conformal η-Ricci soliton on Sasakian manifolds. Here, we discuss some curvature properties on Sasakian manifold admitting *-Conformal η-Ricci soliton. We obtain some significant results on *-Conformal η-Ricci soliton in Sasakian manifolds satisfying R(ξ,X).S = 0, S(ξ,X).R = 0, {\overline}P(ξ,X…

Study on para-Sasakian metrics and their solitons.

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

We find all Ricci semi-symmetric as well as all conformally semi-symmetric spacetimes. Neither of these properties implies the other. We verify that only conformally flat spacetimes can be Ricci semi-symmetric without being conformally semi-symmetric and show that only vacuum spacetimes and spacetimes with just a $Λ$-t…

Classification of specific pseudo-Riemannian manifolds.

In this article we study the short-time existence of conformal Ricci flow on asymptotically hyperbolic manifolds. We also prove a local Shi's type curvature derivative estimate for conformal Ricci flow.

The paper studies geometric structures in perfect fluid spacetimes with specific metrics.

The paper bends Riemannian manifolds to achieve metrics with negative Ricci curvature.

Characterizes potential function of almost conformal Ricci solitons on Sasakian manifolds.

We consider four dimensional conformally flat homogeneous pseudo Riemannian manifolds. According to forms (Seger types) of the Ricci operator, we provide a full classification of four dimensional pseudo Riemannian conformally flat homogeneous Ricci solitons.

In this paper, we first apply an integral identity on Ricci solitons to prove that closed locally conformally flat gradient Ricci solitons are of constant sectional curvature. We then generalize this integral identity to complete noncompact gradient shrinking Ricci solitons, under the conditions that the Ricci curvatur…

In this paper, we investigate the behavior of the normalized Ricci flow on asymptotically hyperbolic manifolds. We show that the normalized Ricci flow exists globally and converges to an Einstein metric when starting from a non-degenerate and sufficiently Ricci pinched metric. More importantly we use maximum principles…

It is proved that every locally conformal flat Riemannian manifold all of whose Jacobi operators have constant eigenvalues along every geodesic is with constant principal Ricci curvatures. A local classification (up to an isometry) of locally conformal flat Riemannian manifold with constant Ricci eigenvalues is given i…

We analyze an energy functional associated to Conformal Ricci Flow along closed manifolds with constant negative scalar curvature. Given initial conditions we use this functional to demonstrate the uniqueness of both the metric and the pressure function along Conformal Ricci Flow.

The paper characterizes contact metric manifolds with specific solitons.

The study classifies gradient Ricci solitons with specific vector fields.

The paper extends Nakamaye's theorem to non-closed forms on complex manifolds.

In this paper we show that all conformal metrics to a pseudo-euclidean space invariant under the translation group, and all the conformal metrics product manifold also invariant by translation where F m it is Ricci flat semi-Riemannian manifold, are gradient Ricci almost soliton. We also proved that all conformal metri…

We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equ…

Study on Kähler-Ricci flow and conformal submersion singularity formation.

We show that any locally conformally flat ancient solution to the Ricci flow must be rotationally symmetric. As a by-product, we prove that any locally conformally flat Ricci soliton is a gradient soliton in the shrinking and steady cases as well as in the expanding case, provided the soliton has nonnegative curvature.

In this note we prove that any four-dimensional half conformally flat gradient steady Ricci soliton must be either Bryant's soliton or Ricci flat. We also classify four-dimensional half conformally flat gradient shrinking Ricci solitons with bounded curvature.

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…

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