Paper · Jan 13, 2018

Ricci solitons in almost -cosymplectic manifolds

Xiaomin Chen

math.DGarXiv:1801.04398v2
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Abstract

In this article we study an almost -cosymplectic manifold admitting a Ricci soliton. We first prove that there do not exist Ricci solitons on an almost cosymplectic -manifold. Further, we consider an almost -cosymplectic manifold admitting a Ricci soliton whose potential vector field is the Reeb vector field and show that a three dimesional almost -cosymplectic is a cosymplectic manifold. Finally we classify a three dimensional -Einstein almost -cosymplectic manifold admitting a Ricci soliton.

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Submitted
Jan 13, 2018
Last revised
Nov 26, 2019 (v2)
Subjects
math.DG
Journal
Bulletin of the Belgian Mathematical Society -- Simon Stevin,Vol. 25 issue 2, 2018

Comments: We correct the Theorem 1.1 and its proof

Ricci solitons3-manifoldsSasakian & 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 Notes on Ricci solitons in f-cosymplectic manifolds (Xiaomin Chen, 2018)1Chen 2018 A note on Ricci soliton in almost Kenmotsu manifold (Fatemah Mofarreh and U. C. De, 2018)5Mofarreh 2018 Certain results on Kenmotsu pseudo-metric manifolds (Devaraja Mallesha Naik, Venkatesha and D. G. Prakasha, 2018)7Naik 2018 *-Ricci solitons and gradient almost *-Ricci solitons on Kenmotsu manifolds (Venkatesha Venkatesh, Devaraja Mallesha Naik and H Aruna Kumara, 2019)2Venkatesh 2019 Ricci ρ-solitons on 3-dimensional η-Einstein almost Kenmotsu mandifolds (Sh. Azami and Gh. Fasihi-Ramandi, 2019)6Azami 2019 Geometry of almost contact metrics as almost *-Ricci solitons (Dhriti Sundar Patra, Akram Ali and Fatemah Mofarreh, 2021)3Patra 2021 η-Ricci solitons on contact pseudo-metric manifolds (Eftekhar Asgharzadeh and Morteza Faghfouri, 2021)8Asgharzadeh 2021 Non-compact Ricci Solitons of Finite Volume with Potential Field of Constant Length (Hemangi Madhusudan Shah, Sharief Deshmukh and Mohammad Aqib, 2026)4Shah 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Notes on Ricci solitons in -cosymplectic manifolds

    Xiaomin Chen

    Topics Sasakian & contact geometry, Ricci solitons · Same author Xiaomin Chen · Shared terms “cosymplectic manifold”, “admitting”

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

    Venkatesha Venkatesh, Devaraja Mallesha Naik and H Aruna Kumara

    Topics Sasakian & contact geometry, 3-manifolds, Ricci solitons · Shared terms “vector field”, “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 · Shared terms “Reeb vector”, “vector field”, “potential vector”

  4. Non-compact Ricci Solitons of Finite Volume with Potential Field of Constant Length

    Hemangi Madhusudan Shah, Sharief Deshmukh and Mohammad Aqib

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

  5. A note on Ricci soliton in almost Kenmotsu manifold

    Fatemah Mofarreh and U. C. De

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

  6. Ricci -solitons on 3-dimensional -Einstein almost Kenmotsu mandifolds

    Sh. Azami and Gh. Fasihi-Ramandi

    Topics Sasakian & contact geometry, 3-manifolds, Ricci solitons · Shared terms “Einstein almost”

  7. Certain results on Kenmotsu pseudo-metric manifolds

    Devaraja Mallesha Naik, Venkatesha and D. G. Prakasha

    Topics Sasakian & contact geometry, 3-manifolds, Ricci solitons · Shared terms “manifold admitting”

  8. Ricci solitons on contact pseudo-metric manifolds

    Eftekhar Asgharzadeh and Morteza Faghfouri

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “manifold admitting”, “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) 3-manifolds Dimension three is where Ricci flow has done its most complete work. It proves geometrization, describes the flow's long-time behaviour, and now… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) 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)

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