Paper · Aug 14, 2020

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

Adara M. Blaga

As on arXiv

Abstract

We consider almost Riemann solitons in a Riemannian manifold and underline their relation to almost Ricci solitons. When is of gradient type, using Bochner formula, we explicitly express the function by means of the gradient vector field and illustrate the result with suitable examples. Moreover, we deduce some properties for the particular cases when the potential vector field of the soliton is solenoidal or torse-forming, with a special view towards curvature.

Submitted
Aug 14, 2020
Last revised
Jan 15, 2021 (v4)
Subjects
math.DG
Journal
Bulletin of the Malaysian Mathematical Sciences Society 44, 3215-3227 (2021)
DOI
10.1007/s40840-021-01108-9

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 On warped product gradient η-Ricci solitons (Adara M. Blaga, 2017)7Blaga 2017 Solitons and geometrical structures in a perfect fluid spacetime (Adara M. Blaga, 2017)8Blaga 2017 η-Ricci solitons in (ε)-almost paracontact metric manifolds (Adara Monica Blaga, Selcen Yüksel Perktaş, Bilal Eftal Acet et al., 2017)3Blaga 2017 Almost η-Ricci solitons in (LCS)ₙ-manifolds (Adara M. Blaga, 2017)6Blaga 2017 Geometric solitons in a D-homothetically deformed Kenmotsu manifold (Adara M. Blaga, 2020)2Blaga 2020 Remarks on Riemann and Ricci solitons in (α,β)-contact metric manifolds (Adara M. Blaga and Dan Radu Latcu, 2020)1Blaga 2020 On conformal collineation and almost Ricci solitons (Adara M. Blaga and Bang-Yen Chen, 2022)4Blaga 2022 On some 3-dimensional almost η-Ricci solitons with diagonal metrics (Adara M. Blaga, 2024)5Blaga 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 Riemann and Ricci solitons in -contact metric manifolds

    Adara M. Blaga and Dan Radu Latcu

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “almost Riemann”, “Riemann solitons”, “vector field”

  2. Geometric solitons in a -homothetically deformed Kenmotsu manifold

    Adara M. Blaga

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “almost Riemann”, “vector field”, “gradient vector”

  3. -Ricci solitons in -almost paracontact metric manifolds

    Adara Monica Blaga, Selcen Yüksel Perktaş, Bilal Eftal Acet et al.

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

  4. On conformal collineation and almost Ricci solitons

    Adara M. Blaga and Bang-Yen Chen

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

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

    Adara M. Blaga

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

  6. Almost -Ricci solitons in -manifolds

    Adara M. Blaga

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “Bochner”

  7. On warped product gradient -Ricci solitons

    Adara M. Blaga

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

  8. Solitons and geometrical structures in a perfect fluid spacetime

    Adara M. Blaga

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

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.

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.