Paper · Jul 14, 2025

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

Murat Altunbaş, Ayşe Karanlık Akpınar

math.DGarXiv:2507.09954v3
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Abstract

We study the properties of LP-Sasakian manifolds endowed with generalized Ricci solitons associated to the general connection. Finally, the existence of such solitons on a 4-dimensional LP-Sasakian manifold is proved by constructing a non-trivial example.

Comments: Some calculation errors

Ricci solitons4-manifoldsSasakian & contact geometry

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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 2021, plus the canon.

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  1. On the Generalised Ricci Solitons and Sasakian Manifolds

    Ahmed Mohammed Cherif, Kaddour Zegga and Gherici Beldjilali PDF

    Topics Sasakian & contact geometry, Ricci solitons

  2. Immersions of Sasaki-Ricci solitons into homogeneous Sasakian manifolds

    Roberto Mossa and Giovanni Placini PDF

    Topics Sasakian & contact geometry, Ricci solitons

  3. Characterization of Sasakian Manifolds by Curvature Conditions

    Sourav Nayak, Vladimir Rovenski and Dhriti Sundar Patra PDF

    Topics Sasakian & contact geometry

  4. Complete gradient Einstein-type Sasakian manifolds with

    Shun Maeta PDF

    Topics Sasakian & contact geometry, Ricci solitons

  5. Geometry of para-Sasakian metric as an almost conformal -Ricci soliton

    Sumanjit Sarkar, Santu Dey and Arindam Bhattacharyya PDF

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

  6. Sasakian lift of Kaehler manifold and -Sasakian Ricci solitons

    Piotr Dacko PDF

    Topics Sasakian & contact geometry, Ricci solitons

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

    Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya PDF

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

  8. -Ricci-Yamabe Soliton and Contact Geometry

    Dibakar Dey PDF

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

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) 4-manifolds Four is the first dimension where Ricci flow's singularities are not fully understood. It is also the dimension of the smooth Poincaré conjecture… Start with: The topology of four-dimensional manifolds (Freedman, 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)

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.