Paper · Mar 13, 2018

Harmonic aspects in an -Ricci soliton

Adara M. Blaga

math.DGarXiv:1803.04679v2
View PDF View HTML arXiv page

As on arXiv

Abstract

We characterize -Ricci solitons in some special cases when the -form , which is the -dual of , is a harmonic or a Schrödinger-Ricci harmonic form. We also provide necessary and sufficient conditions for to be a solution of the Schrödinger-Ricci equation and point out the relation between the three notions in our context. In particular, we apply these results to a perfect fluid spacetime and using Bochner- Weitzenböck techniques, we formulate some more conclusions for gradient solitons and deduce topological properties of the manifold and its universal covering.

View PDF View HTML arXiv page
Submitted
Mar 13, 2018
Last revised
Aug 23, 2020 (v2)
Subjects
math.DG
Journal
International Electronic Journal of Geometry 13(1), 41-49 (2020)
DOI
10.36890/iejg.573919

Comments: 17 pages

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 Solitons and geometrical structures in a perfect fluid spacetime (Adara M. Blaga, 2017)1Blaga 2017 On warped product gradient η-Ricci solitons (Adara M. Blaga, 2017)8Blaga 2017 Almost η-Ricci solitons in (LCS)ₙ-manifolds (Adara M. Blaga, 2017)2Blaga 2017 Remarks on almost Riemann solitons with gradient or torse-forming vector field (Adara M. Blaga, 2020)3Blaga 2020 Perfect fluid spacetimes and gradient solitons (Krishnendu De Uday Chand De, Abdallah Abdelhameed Syied, Nasser Bin Turki et al., 2021)7De 2021 Characterizations of Perfect fluid spacetimes obeying f(𝓡)-gravity equipped with different gradient solitons (Krishnendu De Young Jin Suh and Uday Chand De, 2022)6Suh 2022 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. 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 “fluid spacetime”, “perfect fluid”

  2. Almost -Ricci solitons in -manifolds

    Adara M. Blaga

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

  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 M. Blaga · Shared terms “Bochner”, “relation”

  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 “formulate”

  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

  6. Characterizations of Perfect fluid spacetimes obeying -gravity equipped with different gradient solitons

    Krishnendu De Young Jin Suh and Uday Chand De

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”, “gradient solitons”

  7. Perfect fluid spacetimes and gradient solitons

    Krishnendu De Uday Chand De, Abdallah Abdelhameed Syied, Nasser Bin Turki et al.

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”, “gradient solitons”

  8. On warped product gradient -Ricci solitons

    Adara M. Blaga

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

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.