Paper · Jan 15, 2018

The k-almost Ricci solitons and contact geometry

Amalendu Ghosh, Dhriti Sundar Patra

math.DGarXiv:1801.04767
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Abstract

The aim of this article is to study the k-almost Ricci soliton and k-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact K-contact metric is a k-almost gradient Ricci soliton then it is isometric to a unit sphere S2n+1. Next, we extend this result on a compact k-almost Ricci soliton when the flow vector field X is contact. Finally, we study some special types of k-almost Ricci soliton where the potential vector field X is point wise collinear with the Reeb vector field ξ of the contact metric structure.

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Submitted
Jan 15, 2018
Subjects
math.DG
Journal
J. Korean Math. Soc. 55 (2018), No. 1, pp. 161-174
DOI
10.4134/JKMS.j170103
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 N(k)-contact metric as ∗-conformal Ricci soliton (Dibakar Dey and Pradip Majhi, 2020)5Dey 2020 Almost η-Ricci solitons on Kenmotsu manifolds (Dhriti Sundar Patra and Vladimir Rovenski, 2020)4Patra 2020 Remarks on Riemann and Ricci solitons in (α,β)-contact metric manifolds (Adara M. Blaga and Dan Radu Latcu, 2020)2Blaga 2020 On non-gradient (m,ρ)-quasi-Einstein contact metric manifolds (Dhriti Sundar Patra and Vladimir Rovenski, 2020)1Patra 2020 Geometry of almost contact metrics as almost *-Ricci solitons (Dhriti Sundar Patra, Akram Ali and Fatemah Mofarreh, 2021)3Patra 2021 ∗-Ricci-Yamabe Soliton and Contact Geometry (Dibakar Dey, 2021)6Dey 2021 Characterizations of Almost Ricci Bourguignon Solitons (Mohammad Aqib, Hemangi Madhusudan Shah and Dhriti Sundar Patra, 2025)8Aqib 2025 Characterization of Sasakian Manifolds by Curvature Conditions (Sourav Nayak, Vladimir Rovenski and Dhriti Sundar Patra, 2026)7Nayak 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. On non-gradient -quasi-Einstein contact metric manifolds

    Dhriti Sundar Patra and Vladimir Rovenski

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same author Dhriti Sundar Patra · Shared terms “vector field”, “Reeb vector”, “collinear”

  2. Remarks on Riemann and Ricci solitons in -contact metric manifolds

    Adara M. Blaga and Dan Radu Latcu

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

  3. Geometry of almost contact metrics as almost -Ricci solitons

    Dhriti Sundar Patra, Akram Ali and Fatemah Mofarreh

    Topics Sasakian & contact geometry, Ricci solitons · Same author Dhriti Sundar Patra · Shared terms “Reeb vector”, “vector field”, “potential vector”

  4. Almost -Ricci solitons on Kenmotsu manifolds

    Dhriti Sundar Patra and Vladimir Rovenski

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same author Dhriti Sundar Patra · Shared terms “Reeb vector”, “vector field”, “collinear”

  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”, “gradient Ricci”

  6. -Ricci-Yamabe Soliton and Contact Geometry

    Dibakar Dey

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

  7. Characterization of Sasakian Manifolds by Curvature Conditions

    Sourav Nayak, Vladimir Rovenski and Dhriti Sundar Patra

    Topics Sasakian & contact geometry · Same author Dhriti Sundar Patra · Shared terms “metric structure”

  8. Characterizations of Almost Ricci Bourguignon Solitons

    Mohammad Aqib, Hemangi Madhusudan Shah and Dhriti Sundar Patra

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Dhriti Sundar Patra

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.