Paper · Aug 18, 2018

Certain results on Kenmotsu pseudo-metric manifolds

Devaraja Mallesha Naik, Venkatesha, D. G. Prakasha

math.DGarXiv:1808.06090v3
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Abstract

In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant -sectional curvature, and prove the structure theorem for -conformally flat and -conformally flat Kenmotsu pseudo-metric manifolds. Next, we consider Ricci solitons on this manifolds. In particular, we prove that an -Einstein Kenmotsu pseudo-metric manifold of dimension higher than 3 admitting a Ricci soliton is Einstein, and a Kenmotsu pseudo-metric 3-manifold admitting a Ricci soliton is of constant curvature .

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Submitted
Aug 18, 2018
Last revised
Dec 24, 2019 (v3)
Subjects
math.DG
Journal
Miskolc Math Notes, Vol. 20, No. 2, pp. 1083-1099, (2019)
DOI
10.18514/MMN.2019.2905

Comments: 17 pages

Ricci solitons3-manifoldsSasakian & contact geometry

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  1. Ricci solitons on contact pseudo-metric manifolds

    Eftekhar Asgharzadeh and Morteza Faghfouri

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “pseudo metric”, “manifold admitting”, “Next”

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

    Venkatesha Venkatesh, Devaraja Mallesha Naik and H Aruna Kumara

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

  3. -Ricci Solitons on Kenmotsu 3-Manifolds

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

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

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

  5. Kenmotsu metric as conformal -Ricci soliton

    Dipen Ganguly

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

  6. Ricci solitons in almost -cosymplectic manifolds

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    Topics Sasakian & contact geometry, 3-manifolds, Ricci solitons · Shared terms “manifold admitting”

  7. A note on Ricci soliton in almost Kenmotsu manifold

    Fatemah Mofarreh and U. C. De

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

  8. Realizations of some contact metric manifolds as Ricci soliton real hypersurfaces

    Jong Taek Cho, Takahiro Hashinaga, Akira Kubo et al.

    Topics Sasakian & contact geometry, 3-manifolds, Ricci solitons

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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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