Paper · May 11, 2018

A note on Ricci soliton in almost Kenmotsu manifold

Fatemah Mofarreh, U. C. De

As on arXiv

Abstract

In this short note it is established that there does not exist Ricci soliton with the Reeb potential vector field in an almost Kenmotsu manifold (briefly, ).

Submitted
May 11, 2018
Last revised
Oct 17, 2021 (v2)
Subjects
math.DG

Comments: 5 pages

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 *-Ricci solitons and gradient almost *-Ricci solitons on Kenmotsu manifolds (Venkatesha Venkatesh, Devaraja Mallesha Naik and H Aruna Kumara, 2019)4Venkatesh 2019 Ricci ρ-solitons on 3-dimensional η-Einstein almost Kenmotsu mandifolds (Sh. Azami and Gh. Fasihi-Ramandi, 2019)3Azami 2019 Geometric solitons in a D-homothetically deformed Kenmotsu manifold (Adara M. Blaga, 2020)8Blaga 2020 Almost η-Ricci solitons on Kenmotsu manifolds (Dhriti Sundar Patra and Vladimir Rovenski, 2020)5Patra 2020 Geometry of almost contact metrics as almost *-Ricci solitons (Dhriti Sundar Patra, Akram Ali and Fatemah Mofarreh, 2021)1Patra 2021 *-Conformal η-Ricci soliton within the framework of Kenmotsu manifolds (Sumanjit Sarkar and Santu Dey, 2021)2Sarkar 2021 Kenmotsu metric as conformal η-Ricci soliton (Dipen Ganguly, 2021)7Ganguly 2021 η-Ricci Solitons on Kenmotsu 3-Manifolds (K. De and U. C. De, 2024)6De 2024
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Geometry of almost contact metrics as almost -Ricci solitons

    Dhriti Sundar Patra, Akram Ali and Fatemah Mofarreh

    Topics Sasakian & contact geometry, Ricci solitons · Same author Fatemah Mofarreh · Shared terms “Kenmotsu”, “potential vector”, “Reeb”

  2. -Conformal -Ricci soliton within the framework of Kenmotsu manifolds

    Sumanjit Sarkar and Santu Dey

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “Kenmotsu manifold”, “almost Kenmotsu”, “potential vector”

  3. Ricci -solitons on 3-dimensional -Einstein almost Kenmotsu mandifolds

    Sh. Azami and Gh. Fasihi-Ramandi

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

  4. -Ricci solitons and gradient almost -Ricci solitons on Kenmotsu manifolds

    Venkatesha Venkatesh, Devaraja Mallesha Naik and H Aruna Kumara

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “Kenmotsu manifold”, “potential vector”, “vector field”

  5. Almost -Ricci solitons on Kenmotsu manifolds

    Dhriti Sundar Patra and Vladimir Rovenski

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “Kenmotsu manifold”, “Reeb”, “potential vector”

  6. -Ricci Solitons on Kenmotsu 3-Manifolds

    K. De and U. C. De

    Topics Sasakian & contact geometry, Ricci solitons · Same author U. C. De · Shared terms “Kenmotsu”

  7. Kenmotsu metric as conformal -Ricci soliton

    Dipen Ganguly

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “Kenmotsu manifold”, “potential vector”, “Reeb”

  8. Geometric solitons in a -homothetically deformed Kenmotsu manifold

    Adara M. Blaga

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