Classification of almost Yamabe solitons in Euclidean spaces

Tatsuya Seko; Shun Maeta

Paper · Nov 13, 2017

Classification of almost Yamabe solitons in Euclidean spaces

Tatsuya Seko, Shun Maeta

math.DGarXiv:1711.04428

View PDF View HTML arXiv page

As on arXiv

Abstract

In this paper, we completely classify almost Yamabe solitons on hypersurfaces in Euclidean spaces arisen from the position vector field. Some results of almost Yamabe solitons with a concurrent vector field and almost Yamabe solitons on submanifolds in Riemannian manifolds equipped with a concurrent vector field are also presented. Moreover, we classify complete Ricci solitons on minimal submanifolds in non-positively curved space forms. For almost Yamabe solitons, all of results in this paper can be applied to Yamabe solitons.

View PDF View HTML arXiv page

Submitted: Nov 13, 2017
Subjects: math.DG

Ricci solitons Almost & η-Ricci solitons Sphere theorems Minimal & CMC surfaces

Its neighbourhood

Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2016, plus the canon.

Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other

Classification of generalized Yamabe solitons under vanishing conditions on the Weyl, Cotton, and Cao-Chen tensors
Shun Maeta2021

Topics Almost & η-Ricci solitons, Ricci solitons · Same author Shun Maeta · Shared terms “almost Yamabe”, “Yamabe soliton”, “classify complete”
Structure of generalized Yamabe solitons and its applications
Shun Maeta2022

Topics Almost & η-Ricci solitons, Ricci solitons · Same author Shun Maeta · Shared terms “Yamabe soliton”
Rigidity results for quotient almost Yamabe solitons
Marcelo Bezerra Barboza, Willian Isao Tokura, Elismar Dias Batista et al.2020Wider flows

Topics Almost & η-Ricci solitons · Shared terms “almost Yamabe”, “Yamabe soliton”, “Euclidean”
Classification of gradient Einstein-type Kähler manifolds with $α = 0$
Shun Maeta2025

Topics Almost & η-Ricci solitons, Ricci solitons · Same author Shun Maeta · Shared terms “Yamabe soliton”, “completely classify”
Ricci-Yamabe solitons on the Lie group $\Sol \times R^{n}$
Abdou Bousso and Ameth Ndiaye2026

Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Yamabe soliton”, “vector field”, “equipped”
$η$ -Ricci-Yamabe Soliton on Riemannian Submersions from Riemannian manifolds
Mohd. Danish Siddiqi and Mehmet Akif Akyol2020

Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Yamabe soliton”, “Riemannian manifold”
Complete gradient Einstein-type Sasakian manifolds with $α = 0$
Shun Maeta2025

Topics Almost & η-Ricci solitons, Ricci solitons · Same author Shun Maeta · Shared terms “Yamabe soliton”
Almost Ricci Solitons on Class $A$ Hypersurfaces of Product Spaces
Ahmet Umut Çoraplı, Burcu Bektaş Demirci and Nurettin Cenk Turgay2025

Topics Almost & η-Ricci solitons, Sphere theorems, Ricci solitons · Shared terms “vector field”, “space form”

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Ricci solitons Metrics that change under Ricci flow only by scaling and diffeomorphisms: shrinking, steady or expanding solitons. Start with: The Ricci flow on surfaces (Hamilton, 1988) Almost & η-Ricci solitons Variations on the Ricci soliton equation: let the constant λ become a function (almost solitons), add a term along a contact form (η-Ricci… Start with: Ricci almost solitons (Pigola et al., 2010) Sphere theorems Curvature conditions that force a manifold to be a sphere. Ricci flow settled the 1/4-pinched differentiable sphere theorem, which had been open for… Start with: Minimal Two-Spheres and the Topology of Manifolds with Positive Curvature on Totally Isotropic Two-Planes (Micallef et al., 1988) Minimal & CMC surfaces Minimal surfaces are critical points of area, with zero mean curvature; constant mean curvature (CMC) surfaces are critical for area at fixed volume. Start with: On the structure of manifolds with positive scalar curvature (Schoen et al., 1979)

In the guidebook

11A.11
Hamilton’s 1982 TheoremBook 11A · The Ricci Flow: Existence and Maximum Principles
Positive Ricci curvature in dimension 3 flows to a round metric.
11B.1
Ricci SolitonsBook 11B · Solitons, Compactness and Singularities
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
12B.2
The Asymptotic Soliton and Three-Dimensional ShrinkersBook 12B · κ-Solutions and Surgery
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.

[1] 11A.11
Hamilton’s 1982 TheoremBook 11A · The Ricci Flow: Existence and Maximum Principles
Positive Ricci curvature in dimension 3 flows to a round metric.

[2] 11B.1
Ricci SolitonsBook 11B · Solitons, Compactness and Singularities
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.

[3] 12B.2
The Asymptotic Soliton and Three-Dimensional ShrinkersBook 12B · κ-Solutions and Surgery
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.

Classification of almost Yamabe solitons in Euclidean spaces

Abstract

Connected papers

Background reading

In the guidebook

Keyboard shortcuts

Anywhere

Lists of papers

Guidebook chapters