Paper · Jan 16, 2019

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

Venkatesha Venkatesh, Devaraja Mallesha Naik, H Aruna Kumara

math.DGarXiv:1901.05222
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Abstract

In this paper, we consider -Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if the metric of a Kenmotsu manifold is a -Ricci soliton, then soliton constant is zero. For 3-dimensional case, if admits a -Ricci soliton, then we show that is of constant sectional curvature -1. Next, we show that if admits a -Ricci soliton whose potential vector field is collinear with the characteristic vector field , then is Einstein and soliton vector field is equal to . Finally, we prove that if is a gradient almost -Ricci soliton, then either is Einstein or the potential vector field is collinear with the characteristic vector field on an open set of . We verify our result by constructing examples for both -Ricci soliton and gradient almost -Ricci soliton.

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Submitted
Jan 16, 2019
Subjects
math.DG
Journal
Math. Slovaca, Volume 69, Issue 6, Pages 1447-1458, (2019)
DOI
10.1515/ms-2017-0321

Comments: 12 pages

Ricci solitons3-manifoldsSasakian & 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 A note on Ricci soliton in almost Kenmotsu manifold (Fatemah Mofarreh and U. C. De, 2018)4Mofarreh 2018 Certain results on Kenmotsu pseudo-metric manifolds (Devaraja Mallesha Naik, Venkatesha and D. G. Prakasha, 2018)3Naik 2018 Ricci ρ-solitons on 3-dimensional η-Einstein almost Kenmotsu mandifolds (Sh. Azami and Gh. Fasihi-Ramandi, 2019)8Azami 2019 Geometric solitons in a D-homothetically deformed Kenmotsu manifold (Adara M. Blaga, 2020)7Blaga 2020 Almost η-Ricci solitons on Kenmotsu manifolds (Dhriti Sundar Patra and Vladimir Rovenski, 2020)1Patra 2020 Geometry of almost contact metrics as almost *-Ricci solitons (Dhriti Sundar Patra, Akram Ali and Fatemah Mofarreh, 2021)5Patra 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)6Ganguly 2021
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Almost -Ricci solitons on Kenmotsu manifolds

    Dhriti Sundar Patra and Vladimir Rovenski

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

  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”, “gradient almost”, “vector field”

  3. Certain results on Kenmotsu pseudo-metric manifolds

    Devaraja Mallesha Naik, Venkatesha and D. G. Prakasha

    Topics Sasakian & contact geometry, 3-manifolds, Ricci solitons · Same author Devaraja Mallesha Naik · Shared terms “Kenmotsu”, “Next”, “sectional curvature”

  4. A note on Ricci soliton in almost Kenmotsu manifold

    Fatemah Mofarreh and U. C. De

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

  5. Geometry of almost contact metrics as almost -Ricci solitons

    Dhriti Sundar Patra, Akram Ali and Fatemah Mofarreh

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

  6. Kenmotsu metric as conformal -Ricci soliton

    Dipen Ganguly

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

  7. Geometric solitons in a -homothetically deformed Kenmotsu manifold

    Adara M. Blaga

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

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

    Sh. Azami and Gh. Fasihi-Ramandi

    Topics Sasakian & contact geometry, 3-manifolds, Ricci solitons · Shared terms “Kenmotsu”, “constant sectional”, “sectional curvature”

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) 3-manifolds Dimension three is where Ricci flow has done its most complete work. It proves geometrization, describes the flow's long-time behaviour, and now… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) 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)

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