Paper · Jan 27, 2023

Conformal Ricci solitons on generalized ()-space forms

Mehraj Ahmad Lone, Towseef Ali Wani

math.DGarXiv:2303.10159
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Abstract

In this paper, we study conformal Ricci solitons and conformal gradient Ricci solitons on generalized ()-space forms. The conditions for the solitons to be shrinking, steady, and expanding are derived in terms of conformal pressure p. We show under what conditions a Ricci semi-symmetric generalized ()-space form equipped with a conformal Ricci soliton forms an Einstein manifold.

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Submitted
Jan 27, 2023
Subjects
math.DG
Journal
International Journal of Geometric Methods in Modern Physics Vol. 19, No. 14, 2250226 (2022)
DOI
10.1142/S0219887822502267
Ricci solitonsEinstein metricsAlmost & η-Ricci solitonsSphere theorems

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  1. Curvature tensors and hyperbolic solitons on Lorentzian trans-Sasakian space form

    Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya

    Topics Almost & η-Ricci solitons, Sphere theorems, Ricci solitons · Shared terms “space forms”, “conformal Ricci”, “Einstein”

  2. Hyperbolic solitons on trans-Sasakian space forms and its submanifolds

    Bidhan Mondal, Sibsankar Panda and Nirabhra Basu

    Topics Almost & η-Ricci solitons, Sphere theorems, Ricci solitons · Shared terms “space forms”

  3. K-contact manifolds admitting some geometric solitons with Semi-Symmetric Non-Metric Connection

    Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “semi symmetric”, “conformal Ricci”, “equipped”

  4. Structure of generalized Yamabe solitons and its applications

    Shun Maeta

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “conformal gradient”

  5. Almost Ricci Solitons on Class Hypersurfaces of Product Spaces

    Ahmet Umut Çoraplı, Burcu Bektaş Demirci and Nurettin Cenk Turgay

    Topics Almost & η-Ricci solitons, Sphere theorems, Ricci solitons · Shared terms “space forms”

  6. Manifolds with 1/4-pinched Curvature are Space Forms

    S. Brendle and R. M. SchoenThe canon

    Topics Sphere theorems · Shared terms “space forms”

  7. Back to almost Ricci solitons

    Vladimir Rovenski, Sergey Stepanov and Irina Tsyganok

    Topics Almost & η-Ricci solitons, Einstein metrics, Ricci solitons

  8. On conformal collineation and almost Ricci solitons

    Adara M. Blaga and Bang-Yen Chen

    Topics Almost & η-Ricci solitons, Ricci solitons

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) 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) Sphere theorems Curvature conditions that force a manifold to be a sphere. Ricci flow settled the 1/4-pinched differentiable sphere theorem, which had been open for… Start with: Minimal Two-Spheres and the Topology of Manifolds with Positive Curvature on Totally Isotropic Two-Planes (Micallef et al., 1988)

In the guidebook

  1. 11A.11
    Hamilton’s 1982 TheoremBook 11A · The Ricci Flow: Existence and Maximum Principles

    Positive Ricci curvature in dimension 3 flows to a round metric.

  2. 11B.1
    Ricci SolitonsBook 11B · Solitons, Compactness and Singularities

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

  3. 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.