Paper · Jan 5, 2021

Geometry of almost contact metrics as almost -Ricci solitons

Dhriti Sundar Patra, Akram Ali, Fatemah Mofarreh

math.DGarXiv:2101.01459
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Abstract

In the present paper, we give some characterizations by considering -Ricci soliton as a Kenmotsu metric. We prove that if a Kenmotsu manifold represents an almost -Ricci soliton with the potential vector field is a Jacobi along the Reeb vector field, then it is a steady -Ricci soliton. Next, we show that a Kenmotsu matric endowed an almost -Ricci soliton is Einstein metric if it is -Einstein or the potential vector field is collinear to the Reeb vector field or is an infinitesimal contact transformation.

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Submitted
Jan 5, 2021
Subjects
math.DG, math.AP

Comments: 12 pages. arXiv admin note: text overlap with arXiv:2008.12497

Ricci solitonsEinstein metricsSasakian & contact geometry

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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 The k-almost Ricci solitons and contact geometry (Amalendu Ghosh and Dhriti Sundar Patra, 2018)3Ghosh 2018 A note on Ricci soliton in almost Kenmotsu manifold (Fatemah Mofarreh and U. C. De, 2018)2Mofarreh 2018 *-Ricci solitons and gradient almost *-Ricci solitons on Kenmotsu manifolds (Venkatesha Venkatesh, Devaraja Mallesha Naik and H Aruna Kumara, 2019)8Venkatesh 2019 Almost η-Ricci solitons on Kenmotsu manifolds (Dhriti Sundar Patra and Vladimir Rovenski, 2020)1Patra 2020 On non-gradient (m,ρ)-quasi-Einstein contact metric manifolds (Dhriti Sundar Patra and Vladimir Rovenski, 2020)4Patra 2020 η-Ricci solitons on contact pseudo-metric manifolds (Eftekhar Asgharzadeh and Morteza Faghfouri, 2021)6Asgharzadeh 2021 *-Conformal η-Ricci soliton within the framework of Kenmotsu manifolds (Sumanjit Sarkar and Santu Dey, 2021)5Sarkar 2021 Kenmotsu metric as conformal η-Ricci soliton (Dipen Ganguly, 2021)7Ganguly 2021
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Almost -Ricci solitons on Kenmotsu manifolds

    Dhriti Sundar Patra and Vladimir Rovenski

    Topics Sasakian & contact geometry, Einstein metrics, Ricci solitons · Same author Dhriti Sundar Patra · Shared terms “Kenmotsu”, “Reeb vector”, “infinitesimal contact”

  2. A note on Ricci soliton in almost Kenmotsu manifold

    Fatemah Mofarreh and U. C. De

    Topics Sasakian & contact geometry, Ricci solitons · Same author Fatemah Mofarreh · Shared terms “Kenmotsu”, “potential vector”, “Reeb”

  3. The k-almost Ricci solitons and contact geometry

    Amalendu Ghosh and Dhriti Sundar Patra

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

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

    Dhriti Sundar Patra and Vladimir Rovenski

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

  5. -Conformal -Ricci soliton within the framework of Kenmotsu manifolds

    Sumanjit Sarkar and Santu Dey

    Topics Sasakian & contact geometry, Einstein metrics, Ricci solitons · Shared terms “Kenmotsu”, “vector field”, “potential vector”

  6. Ricci solitons on contact pseudo-metric manifolds

    Eftekhar Asgharzadeh and Morteza Faghfouri

    Topics Sasakian & contact geometry, Einstein metrics, Ricci solitons · Shared terms “potential vector”, “vector field”, “Reeb vector”

  7. Kenmotsu metric as conformal -Ricci soliton

    Dipen Ganguly

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “Kenmotsu”, “Reeb vector”, “vector field”

  8. -Ricci solitons and gradient almost -Ricci solitons on Kenmotsu manifolds

    Venkatesha Venkatesh, Devaraja Mallesha Naik and H Aruna Kumara

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “Kenmotsu”, “potential vector”, “vector field”

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) Einstein metrics Metrics whose Ricci curvature is a constant multiple of the metric. They are the fixed points of normalised Ricci flow, and the most natural metrics… Start with: On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I (Yau, 1978) 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.