Paper · Feb 8, 2019

Riemannian Submersions Whose Total Manifolds Admitting a Ricci Soliton

Şemsi Eken Meriç, Erol Kılıç

math.DGarXiv:1902.03008v5
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Abstract

In this paper, we study Riemannian submersions whose total manifolds admitting a Ricci soliton. Here, we characterize any fiber of such a submersion is Ricci soliton or almost Ricci soliton. Indeed, we obtain necessary conditions for which the target manifold of Riemannian submersion is a Ricci soliton. Moreover, we study the harmonicity of Riemannian submersion from Ricci soliton and give a characterization for such a submersion to be harmonic.

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Submitted
Feb 8, 2019
Last revised
Jun 26, 2020 (v5)
Subjects
math.DG

Comments: This paper is published on International Journal of Geometric Methods in Modern Physics

Ricci solitonsAlmost & η-Ricci solitons

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 Almost η-Ricci solitons in (LCS)ₙ-manifolds (Adara M. Blaga, 2017)8Blaga 2017 Basic structural equations for almost Ricci-harmonic solitons and applications (Abimbola Abolarinwa, 2018)6Abolarinwa 2018 η-Ricci-Yamabe Soliton on Riemannian Submersions from Riemannian manifolds (Mohd. Danish Siddiqi and Mehmet Akif Akyol, 2020)2Siddiqi 2020 Conformal Submersions Whose Total Manifolds Admit a Ricci Soliton (Kiran Meena and Akhilesh Yadav, 2022)1Meena 2022 On conformal collineation and almost Ricci solitons (Adara M. Blaga and Bang-Yen Chen, 2022)5Blaga 2022 Back to almost Ricci solitons (Vladimir Rovenski, Sergey Stepanov and Irina Tsyganok, 2023)7Rovenski 2023 Nature of Some Solitons on Almost coKähler Manifolds and Asymptotically Harmonic Manifolds (Paritosh Ghosh, Hemangi Madhusudan Shah and Arindam Bhattacharyya, 2023)4Ghosh 2023 Clairaut conformal submersions from Ricci solitons (Murat Polat, 2023)3Polat 2023
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Conformal Submersions Whose Total Manifolds Admit a Ricci Soliton

    Kiran Meena and Akhilesh Yadav

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “total manifolds”, “submersion”, “necessary condition”

  2. -Ricci-Yamabe Soliton on Riemannian Submersions from Riemannian manifolds

    Mohd. Danish Siddiqi and Mehmet Akif Akyol

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Riemannian submersion”, “target manifold”

  3. Clairaut conformal submersions from Ricci solitons

    Murat Polat

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “total manifolds”, “submersion”, “necessary condition”

  4. Nature of Some Solitons on Almost coKähler Manifolds and Asymptotically Harmonic Manifolds

    Paritosh Ghosh, Hemangi Madhusudan Shah and Arindam Bhattacharyya

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “manifold admitting”

  5. On conformal collineation and almost Ricci solitons

    Adara M. Blaga and Bang-Yen Chen

    Topics Almost & η-Ricci solitons, Ricci solitons

  6. Basic structural equations for almost Ricci-harmonic solitons and applications

    Abimbola Abolarinwa

    Topics Almost & η-Ricci solitons, Ricci solitons

  7. Back to almost Ricci solitons

    Vladimir Rovenski, Sergey Stepanov and Irina Tsyganok

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

  8. Almost -Ricci solitons in -manifolds

    Adara M. Blaga

    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) 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)

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.