Paper · Jul 24, 2017

-Ricci solitons in -almost paracontact metric manifolds

Adara Monica Blaga, Selcen Yüksel Perktaş, Bilal Eftal Acet, Feyza Esra Erdoğan

math.DGarXiv:1707.07528v2
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Abstract

The object of this paper is to study -Ricci solitons on -almost paracontact metric manifolds. We investigate -Ricci solitons in the case when its potential vector field is exactly the characteristic vector field of the -almost paracontact metric manifold and when the potential vector field is torse-forming. We also study Einstein-like and -para Sasakian manifolds admitting -Ricci solitons. Finally we obtain some results for -Ricci solitons on -almost paracontact metric manifolds with a special view towards parallel symmetric (0,2)-tensor fields.

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Submitted
Jul 24, 2017
Last revised
Jul 25, 2017 (v2)
Subjects
math.DG
Journal
Glasnik Matematicki 53(1), 205-220 (2018)
DOI
10.3336/gm.53.1.14

Comments: 20 pages

Ricci solitonsAlmost & η-Ricci solitonsSasakian & 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 Para-Sasakian manifolds and *-Ricci solitons (D. G. Prakasha and Pundikala Veeresha, 2018)5Prakasha 2018 The k-almost Ricci solitons and contact geometry (Amalendu Ghosh and Dhriti Sundar Patra, 2018)7Ghosh 2018 Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds (Adara M. Blaga and Selcen Yuksel Perktas, 2018)1Blaga 2018 Geometric solitons in a D-homothetically deformed Kenmotsu manifold (Adara M. Blaga, 2020)4Blaga 2020 Remarks on almost Riemann solitons with gradient or torse-forming vector field (Adara M. Blaga, 2020)3Blaga 2020 Remarks on Riemann and Ricci solitons in (α,β)-contact metric manifolds (Adara M. Blaga and Dan Radu Latcu, 2020)2Blaga 2020 On conformal collineation and almost Ricci solitons (Adara M. Blaga and Bang-Yen Chen, 2022)8Blaga 2022 On some 3-dimensional almost η-Ricci solitons with diagonal metrics (Adara M. Blaga, 2024)6Blaga 2024
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Remarks on almost -Ricci solitons in -para Sasakian manifolds

    Adara M. Blaga and Selcen Yuksel Perktas

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same authors Adara Monica Blaga, Selcen Yüksel Perktaş · Shared terms “para Sasakian”

  2. Remarks on Riemann and Ricci solitons in -contact metric manifolds

    Adara M. Blaga and Dan Radu Latcu

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same author Adara Monica Blaga · Shared terms “potential vector”, “vector field”

  3. Remarks on almost Riemann solitons with gradient or torse-forming vector field

    Adara M. Blaga

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara Monica Blaga · Shared terms “torse forming”, “special view”, “view towards”

  4. Geometric solitons in a -homothetically deformed Kenmotsu manifold

    Adara M. Blaga

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same author Adara Monica Blaga · Shared terms “vector field”, “potential vector”

  5. Para-Sasakian manifolds and *-Ricci solitons

    D. G. Prakasha and Pundikala Veeresha

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “para Sasakian”, “paracontact”

  6. On some -dimensional almost -Ricci solitons with diagonal metrics

    Adara M. Blaga

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara Monica Blaga · Shared terms “potential vector”, “vector field”

  7. The k-almost Ricci solitons and contact geometry

    Amalendu Ghosh and Dhriti Sundar Patra

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “vector field”, “potential vector”

  8. On conformal collineation and almost Ricci solitons

    Adara M. Blaga and Bang-Yen Chen

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara Monica Blaga · Shared terms “potential vector”, “vector field”

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) 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.