Paper · Sep 5, 2020

Remarks on Riemann and Ricci solitons in -contact metric manifolds

Adara M. Blaga, Dan Radu Latcu

math.DGarXiv:2009.02506v4
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Abstract

We study almost Riemann solitons and almost Ricci solitons in an -contact metric manifold satisfying some Ricci symmetry conditions, treating the case when the potential vector field of the soliton is pointwise collinear with the structure vector field.

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Submitted
Sep 5, 2020
Last revised
Jan 15, 2021 (v4)
Subjects
math.DG
Journal
Journal of Geometry and Symmetry in Physics 58, 1-12 (2020)
DOI
10.7546/jgsp-58-2020-1-12
Ricci solitonsAlmost & η-Ricci solitonsSasakian & contact geometry

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 η-Ricci solitons in (ε)-almost paracontact metric manifolds (Adara Monica Blaga, Selcen Yüksel Perktaş, Bilal Eftal Acet et al., 2017)2Blaga 2017 The k-almost Ricci solitons and contact geometry (Amalendu Ghosh and Dhriti Sundar Patra, 2018)1Ghosh 2018 Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds (Adara M. Blaga and Selcen Yuksel Perktas, 2018)7Blaga 2018 N(k)-contact metric as ∗-conformal Ricci soliton (Dibakar Dey and Pradip Majhi, 2020)5Dey 2020 Geometric solitons in a D-homothetically deformed Kenmotsu manifold (Adara M. Blaga, 2020)3Blaga 2020 Remarks on almost Riemann solitons with gradient or torse-forming vector field (Adara M. Blaga, 2020)4Blaga 2020 On non-gradient (m,ρ)-quasi-Einstein contact metric manifolds (Dhriti Sundar Patra and Vladimir Rovenski, 2020)6Patra 2020 On conformal collineation and almost Ricci solitons (Adara M. Blaga and Bang-Yen Chen, 2022)8Blaga 2022
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. The k-almost Ricci solitons and contact geometry

    Amalendu Ghosh and Dhriti Sundar Patra

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “vector field”, “collinear”, “potential vector”

  2. -Ricci solitons in -almost paracontact metric manifolds

    Adara Monica Blaga, Selcen Yüksel Perktaş, Bilal Eftal Acet et al.

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “potential vector”, “vector field”

  3. Geometric solitons in a -homothetically deformed Kenmotsu manifold

    Adara M. Blaga

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “almost Riemann”, “vector field”, “potential vector”

  4. Remarks on almost Riemann solitons with gradient or torse-forming vector field

    Adara M. Blaga

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “almost Riemann”, “Riemann solitons”, “vector field”

  5. -contact metric as -conformal Ricci soliton

    Dibakar Dey and Pradip Majhi

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “vector field”

  6. On non-gradient -quasi-Einstein contact metric manifolds

    Dhriti Sundar Patra and Vladimir Rovenski

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “vector field”, “collinear”, “potential vector”

  7. Remarks on almost -Ricci solitons in -para Sasakian manifolds

    Adara M. Blaga and Selcen Yuksel Perktas

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “manifolds satisfying”

  8. On conformal collineation and almost Ricci solitons

    Adara M. Blaga and Bang-Yen Chen

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “vector field”, “potential vector”

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) Sasakian & contact geometry Sasakian manifolds are odd-dimensional manifolds whose metric cone is Kähler. They carry a transverse Kähler structure, so Kähler–Ricci flow has an… Start with: THE SASAKI–RICCI FLOW (SMOCZYK et al., 2010)

In the guidebook

  1. 11B.1
    Ricci SolitonsBook 11B · Solitons, Compactness and Singularities

    Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.

  2. 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.