arXiv research

3D steady gradient Ricci solitons are all O(2)-symmetric.

Researchers discover a new family of 3D solitons that are flying wings.

The only known example of collapsed three-dimensional complete gradient steady Ricci solitons so far is the 3D cigar soliton $N^2\times \mathbb{R}$, the product of Hamilton's cigar soliton $N^2$ and the real line $\mathbb{R}$ with the product metric. R. Hamilton has conjectured that there should exist a family of colla…

The paper classifies 3D complete gradient Yamabe solitons.

3D flying wings created for any angle asymptotic cones.

The two-loop renormalization group flow is studied via the induced bracket flow on 3D unimodular Lie groups. A number of steady solitons are found. Some of these steady solitons come from maximally symmetric metrics that are steady, shrinking, or expanding solitons under Ricci flow, while others are not obviously relat…

Study properties of 3D trans-Sasakian manifolds with η-Yamabe solitons.

3D solitons classified into specific types.

Study classifies Riemann solitons on specific 3D Lorentzian groups.

Researchers found explicit formulae for special solitons in 3D spaces.

Study 4D steady gradient Ricci solitons reducing to 3D manifolds.

The paper classifies special geometric shapes in 2D and 3D.

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

Study on Ricci solitons and related metrics in 3D trans-Sasakian manifolds.

Defines and classifies algebraic Schouten solitons in 3D Lorentzian Lie groups.

Study of 4D Ricci solitons with symmetry, finding precise geometric asymptotics.

This paper has been withdrawn by the author due to an error

Paper classifies 3D breathers and generalizes Ricci soliton results.

In this note, we prove that a 3-dimensional steady Ricci soliton is rotationally symmetric if its scalar curvature $R(x)$ satisfies $\frac{C_0^{-1}}{ρ(x)}\le R(x)\le \frac{C_0}{ρ(x)}$ for some constant $C_0>0$, where $ρ(x)$ denotes the distance from a fixed point $x_0$. Our result doesn't assume that the soliton is $…

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

Researchers find limits on curvature of certain 3D solitons.

Researchers found cylindrical steady gradient solitons in 3D.

The study finds Ricci solitons on a specific type of 3D Lorentzian Walker manifold.

The study classifies translating and self-expanding solitons in 3D space.

Study properties of 3D almost η-Ricci solitons with diagonal metrics.

The study of quasi Yamabe solitons on 3D contact metric manifolds with specific curvature condition.

In this paper we use the anholonomic frames method to construct exact solutions for vacuum 5D gravity with metrics having off-diagonal components. The solutions are in general anisotropic and possess interesting features such as an anisotropic warp factor with respect to the extra dimension, or a gravitational scaling/…

Let $(M^3, g, f)$ be a nontrivial 3-dimensional steady gradient Ricci soliton. If the scalar curvature $R$ satisfies $c_1r^{-b}\leq R\leq c_2r^{-a}$ for some $a\in(0,1], b\geq a$, and $c_1,c_2>0$, then the umbilical ratio of the level sets of $f$ satisfies $\frac{2|A|^2-H^2}{H^2}\in O(r^{6a-\frac{8a^2}{b}})\cap O(r^{2b…

Survey classifies singularity models in 3D Ricci flow.

The study provides estimates for curvature of gradient Ricci solitons.

Study null curves and their motion in 3D flat space-time, leading to integrable hierarchies.

Let $(M^n,g,\nabla f)$, $n\geq 3$, be an expanding gradient Ricci soliton with nonnegative sectional curvature whose asymptotic cone is isometric to $C(\mathbb{S}^{n-1}(c))$ where $\mathbb{S}^{n-1}(c)$ is the standard $(n-1)$-sphere of curvature $1/c^2$, with $c\in(0,1)$. We prove that if the convergence to the asympto…

We construct a new class of exact solutions describing spacetimes possessing Lie algebroid symmetry. They are described by generic off-diagaonal 5D metrics embedded in bosonic string gravity and possess nontrivial limits to the Einstein gravity. While we focus on nonholonomic vielbein transforms of the Schwarzschild me…

Study of Yamabe solitons on specific geometric manifolds.

Solitary waves are localized gravity waves that preserve their consistency and henceforth their visibility through properties of nonlinear hydrodynamics. Solitary waves have finite amplitude and spread with constant speed and constant shape. In this paper, we have used Lie group of transformation method to solve (3 + 1…

The paper proves smoothness of mean curvature flow for generic initial data in 3D and 4D.

Study surfaces with specific curvature properties in 3D space.

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.