arXiv research

Left-invariant Cotton solitons on homogeneous manifolds are determined. Moreover, algebraic Cotton solitons are studied providing examples of non-invariant Cotton solitons, both in the Riemannian and Lorentzian homogeneous settings.

The paper studies Cotton solitons on specific geometric manifolds.

In this paper, we classify 3-dimensional complete gradient Yamabe solitons with divergence-free Cotton tensor. We also give some classifications of complete gradient Yamabe solitons with nonpositively curved Ricci curvature in the direction of the gradient of the potential function.

This paper classifies solitons under specific tensor conditions.

Extends soliton theory to non-compact cases.

We classify complete gradient Ricci solitons satisfying a fourth-order vanishing condition on the Weyl tensor, improving previously known results. More precisely, we show that any $n$-dimensional ($n\geq 4$) gradient shrinking Ricci soliton with fourth order divergence-free Weyl tensor is either Einstein, or a finite q…

k-Curvature homogeneous three-dimensional Walker metrics are described for k=0,1,2. This allows a complete description of locally homogeneous three-dimensional Walker metrics, showing that there exist exactly three isometry classes of such manifolds. As an application one obtains a complete description of all locally h…

Compact 3D Cotton-parallel manifolds are always conformally flat.

Study on the geometry of Cotton gravity field equations.

Study Codazzi tensors in space-times, linking to Cotton gravity.

Using the conformally invariant Cotton tensor, we define a geometric flow, the "Cotton flow", which is exclusive to three dimensions. This flow tends to evolve the initial metrics into conformally flat ones, and is somewhat orthogonal to the Yamabe flow, the latter being a flow within a conformal class. We define an en…

We study the deformation of the three-dimensional conformal structures by the Ricci flow. We drive the evolution equation of Cotton-York tensor and the L1-norm of it under the Ricci flow. In particular, we investigate the behavior of the L1-norm of the Cotton-York tensor under the Ricci flow on three-dimensional simply…

Chern-Simons invariants of closed oriented Riemannian $3$-manifolds are introduced and studied from the basics. Their first-order variation is the Cotton tensor. The properties of the Cotton tensor: symmetry, conformal covariance, trace- and divergence-freedom, are recovered as corollaries of the Chern-Simons invariant…

We compute the evolution equation of the Cotton and the Bach tensor under the Ricci flow of a Riemannian manifold, with particular attention to the three dimensional case, and we discuss some applications.

Introduces a new tensor for electrostatic systems in arbitrary dimensions.

This paper presents conformal invariants for Riemannian manifolds of dimension greater than or equal to four whose vanishing is necessary for a Riemannian manifold to be conformally related to an Einstein space. One of the invariants is a modification of the Cotton tensor, the other is a $n$--dimensional version of the…

A necessary and sufficient condition for the leaves of a {\em non-degenerate} foliation of a pseudo-Riemannian manifold to be conformally flat is developed. The condition mimics the classical condition of the vanishing of the Weyl or Cotton tensor establishing the conformal flatness of a pseudo-Riemannian manifold in t…

New methods incorporate alpha signals into portfolio construction, improving performance.

Paper uses LSTM neural networks to forecast commodity prices.

We consider instanton solutions of Euclidean Horava-Lifshitz gravity in four dimensions satisfying the detailed balance condition. They are described by geometric flows in three dimensions driven by certain combinations of the Cotton and Ricci tensors as well as the cosmological-constant term. The deformation curvature…

The paper classifies electrovacuum spaces in higher dimensions, proving several key results.

The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent H_s=1/2, when the increments are nonstationary, as they are in FX markets. The nonstationarity arises from s…

In this article we introduce local gauge conditions under which many curvature tensors appearing in conformal geometry, such as the Weyl, Cotton, Bach, and Fefferman-Graham obstruction tensors, become elliptic operators. The gauge conditions amount to fixing an $n$-harmonic coordinate system and normalizing the determi…

We solve the classifying problem raised by Fischer and Marsden for Bach flat static spaces. We also prove the conjecture about critical point equations proposed by Besse for Bach flat manifolds. Particularly in dimension 3, we derive an integral identity that allows us to obtain conformal flatness from the vanish of th…

We investigate the structure of conformal $C$-spaces,a class of Riemmanian manifolds which naturally arises as aconformal generalisation of the Einstein condition. A basic question is when such a structure is closed, or equivalently locally conformally Cotton. In dimension 4 we obtain a full answer to this question and…

In the Cauchy problem for asymptotically flat vacuum data the solution-jets along the cylinder at space-like infinity develop in general logarithmic singularities at the critical sets at which the cylinder touches future/past null infinity. The tendency of these singularities to spread along the null generators of null…

We provide an explicit formula for the Fefferman-Graham-ambient metric of an $n$-dimensional conformal $pp$-wave in those cases where it exists. In even dimensions we calculate the obstruction explicitly. Furthermore, we describe all 4-dimensional $pp$-waves that are Bach-flat, and give a large class of Bach-flat examp…

We study transverse-tracefree (TT)-tensors on conformally flat 3-manifolds $(M,g)$. The Cotton-York tensor linearized at $g$ maps every symmetric tracefree tensor into one which is TT. The question as to whether this is the general solution to the TT-condition is viewed as a cohomological problem within an elliptic com…

The paper classifies a type of solitons in Euclidean spaces.

Study on shrinking solitons of generalized Ricci flow.

New examples of solitons found as warped products.

Study on Yamabe solitons with applications and structure elucidation.

We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups. All algebraic Ricci solitons that we obtain are sol-solitons. In particular, we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not to be algebraic Ricci solitons. We classify Algebraic Ricci Solitons of three-d…

The study examines Riemann solitons and almost solitons on specific Kenmotsu manifolds.

Study on $η$-Ricci-Yamabe solitons on Riemannian submersions.

Study on geometric properties of second Ricci solitons.

Study on Ricci-like solitons and gradient solitons on specific manifolds.

The study classifies steady Ricci solitons based on geometric conditions.

Study on p-biharmonic maps from gradient Ricci solitons, focusing on 2D cigar soliton.

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

We prove some results for the solitons of the Ricci-Bourguignon flow, generalizing corresponding results for Ricci solitons. Taking motivation from Ricci almost solitons, we then introduce the notion of Ricci-Bourguignon $almost$ solitons and prove some results about them which generalize previous results for Ricci alm…

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

Researchers study solitons on homogeneous manifolds, proving properties of specific types of solitons.

The paper characterizes Ricci solitons on the Poincaré upper half plane.

Characterizes $*$-$k$-Ricci-Yamabe solitons on Kenmotsu manifolds.

The paper explores almost Ricci solitons on Finsler spaces, proving conditions for their existence.

New families of Ricci solitons found with collapsing volume.

The study classifies h-almost Ricci-Yamabe solitons in various paracontact manifolds.