Paper · Jan 17, 2018

Notes on Ricci solitons in -cosymplectic manifolds

Xiaomin Chen

math.DGarXiv:1801.05530
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Abstract

The purpose of this article is to study an -cosymplectic manifold admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons on -cosymplectic manifolds. One is the class of contact Ricci solitons. The other is the class of gradient Ricci solitons, for which we give the local classifications of . Meanwhile, we also give some properties of -cosymplectic manifolds.

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Submitted
Jan 17, 2018
Subjects
math.DG
Journal
Journal of Mathematical Physics, Analysis, Geometry,2017, Vol 13, No.3, 242-253
DOI
10.15407/mag13.03.242
Ricci solitonsSasakian & contact geometry

Its neighbourhood

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  1. Ricci solitons in almost -cosymplectic manifolds

    Xiaomin Chen

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

  2. 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”, “admitting”

  3. A note on Ricci soliton in almost Kenmotsu manifold

    Fatemah Mofarreh and U. C. De

    Topics Sasakian & contact geometry, Ricci solitons

  4. Ricci solitons on contact pseudo-metric manifolds

    Eftekhar Asgharzadeh and Morteza Faghfouri

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “admitting”

  5. Kähler Gradient Ricci Solitons with Large Symmetry

    Hung Tran

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “gradient Ricci”

  6. Gradient Shrinking Sasaki-Ricci Solitons with Harmonic Weyl Tensor

    Shu-Cheng Chang and Hongbing Qiu

    Topics Sasakian & contact geometry, Ricci solitons

  7. Generalized Ricci solitons on LP-Sasakian manifolds admitting the general connection

    Murat Altunbaş and Ayşe Karanlık Akpınar

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “admitting”

  8. -contact metric as -conformal Ricci soliton

    Dibakar Dey and Pradip Majhi

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “admitting”, “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.

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) 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.