Paper · Jun 17, 2016

Special solitons on 3-manifolds

Nasrin Malekzadeh, Esmaiel Abedi

As on arXiv

Abstract

In this paper, we study solitons on -dimensional manifolds. In particular, we show that -dimensional pseudo-symmetric gradient Ricci solitons and nontrivial gradient Yamabe solitons are locally isometric to either , , , or .

Submitted
Jun 17, 2016
Subjects
math.DG

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.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Three-dimensional Ricci-degenerate Riemannian manifolds satisfying geometric equations (Jinwoo Shin, 2018)8Shin 2018 η-Ricci-Yamabe Soliton on Riemannian Submersions from Riemannian manifolds (Mohd. Danish Siddiqi and Mehmet Akif Akyol, 2020)4Siddiqi 2020 N(k)-contact metric as ∗-conformal Ricci soliton (Dibakar Dey and Pradip Majhi, 2020)5Dey 2020 Classification of generalized Yamabe solitons under vanishing conditions on the Weyl, Cotton, and Cao-Chen tensors (Shun Maeta, 2021)7Maeta 2021 ∗-Ricci-Yamabe Soliton and Contact Geometry (Dibakar Dey, 2021)6Dey 2021 Structure of generalized Yamabe solitons and its applications (Shun Maeta, 2022)1Maeta 2022 Investigations on a Riemannian manifold with a semi-symmetric non-metric connection and gradient solitons (Krishnendu De, Uday Chand De and Aydin Gezer, 2024)2De 2024 Ricci-Yamabe solitons on the Lie group Sol × ℝⁿ (Abdou Bousso and Ameth Ndiaye, 2026)3Bousso 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Structure of generalized Yamabe solitons and its applications

    Shun Maeta

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “gradient Yamabe”, “Yamabe soliton”

  2. Investigations on a Riemannian manifold with a semi-symmetric non-metric connection and gradient solitons

    Krishnendu De, Uday Chand De and Aydin Gezer

    Topics Almost & η-Ricci solitons, 3-manifolds, Ricci solitons · Shared terms “gradient Yamabe”, “Yamabe soliton”, “gradient Ricci”

  3. Ricci-Yamabe solitons on the Lie group

    Abdou Bousso and Ameth Ndiaye

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Yamabe soliton”, “gradient Ricci”

  4. -Ricci-Yamabe Soliton on Riemannian Submersions from Riemannian manifolds

    Mohd. Danish Siddiqi and Mehmet Akif Akyol

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Yamabe soliton”

  5. -contact metric as -conformal Ricci soliton

    Dibakar Dey and Pradip Majhi

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “dimensional manifolds”, “locally isometric”, “gradient Ricci”

  6. -Ricci-Yamabe Soliton and Contact Geometry

    Dibakar Dey

    Topics Almost & η-Ricci solitons, 3-manifolds, Ricci solitons · Shared terms “Yamabe soliton”, “locally isometric”

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

    Shun Maeta

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Yamabe soliton”, “gradient Yamabe”, “nontrivial”

  8. Three-dimensional Ricci-degenerate Riemannian manifolds satisfying geometric equations

    Jinwoo Shin

    Topics Almost & η-Ricci solitons, 3-manifolds, Ricci solitons · Shared terms “gradient Ricci”

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.

In the guidebook

  1. 10A.1
    A Zoo of Three-ManifoldsBook 10A · Three-Manifolds and Geometrization

    The 3-sphere, lens spaces, the Poincaré sphere, the Hopf fibration and the shape of space.

  2. 10A.2
    Finite Rotation Groups and Spherical Space FormsBook 10A · Three-Manifolds and Geometrization

    Klein's classification by counting poles, the binary groups, and every quotient of the round 3-sphere.

  3. 10A.4
    Homotopy Groups, Degree and the Hurewicz TheoremBook 10A · Three-Manifolds and Geometrization

    Spheres mapped into manifolds: the algebraic topology that finite extinction runs on.