• Title/Summary/Keyword: h-almost Ricci soliton

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RIEMANNIAN SUBMERSIONS WHOSE TOTAL MANIFOLD ADMITS h-ALMOST RICCI-YAMABE SOLITON

  • Mehraj Ahmad Lone;Towseef Ali Wani
    • Communications of the Korean Mathematical Society
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    • v.39 no.2
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    • pp.479-492
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    • 2024
  • In this paper, we study Riemannian submersions whose total manifold admits h-almost Ricci-Yamabe soliton. We characterize the fibers of the submersion and see under what conditions the fibers form h-almost Ricci-Yamabe soliton. Moreover, we find the necessary condition for the base manifold to be an h-almost Ricci-Yamabe soliton and Einstein manifold. Later, we compute scalar curvature of the total manifold and using this we find the necessary condition for h-almost Yamabe solition to be shrinking, expanding and steady. At the end, we give a non-trivial example.

h-almost Ricci Solitons on Generalized Sasakian-space-forms

  • Doddabhadrappla Gowda, Prakasha;Amruthalakshmi Malleshrao, Ravindranatha;Sudhakar Kumar, Chaubey;Pundikala, Veeresha;Young Jin, Suh
    • Kyungpook Mathematical Journal
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    • v.62 no.4
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    • pp.715-728
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    • 2022
  • The aim of this article is to study the h-almost Ricci solitons and h-almost gradient Ricci solitons on generalized Sasakian-space-forms. First, we consider h-almost Ricci soliton with the potential vector field V as a contact vector field on generalized Sasakian-space-form of dimension greater than three. Next, we study h-almost gradient Ricci solitons on a three-dimensional quasi-Sasakian generalized Sasakian-space-form. In both the cases, several interesting results are obtained.

GRADIENT RICCI ALMOST SOLITONS ON TWO CLASSES OF ALMOST KENMOTSU MANIFOLDS

  • Wang, Yaning
    • Journal of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.1101-1114
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    • 2016
  • Let ($M^{2n+1}$, ${\phi}$, ${\xi}$, ${\eta}$, g) be a (k, ${\mu}$)'-almost Kenmotsu manifold with k < -1 which admits a gradient Ricci almost soliton (g, f, ${\lambda}$), where ${\lambda}$ is the soliton function and f is the potential function. In this paper, it is proved that ${\lambda}$ is a constant and this implies that $M^{2n+1}$ is locally isometric to a rigid gradient Ricci soliton ${\mathbb{H}}^{n+1}(-4){\times}{\mathbb{R}}^n$, and the soliton is expanding with ${\lambda}=-4n$. Moreover, if a three dimensional Kenmotsu manifold admits a gradient Ricci almost soliton, then either it is of constant sectional curvature -1 or the potential vector field is pointwise colinear with the Reeb vector field.

SOME RESULTS ON ALMOST KENMOTSU MANIFOLDS WITH GENERALIZED (k, µ)'-NULLITY DISTRIBUTION

  • De, Uday Chand;Ghosh, Gopal
    • Communications of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.1289-1301
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    • 2019
  • In the present paper, we prove that if there exists a second order parallel tensor on an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}$-nullity distribution and $h^{\prime}{\neq}0$, then either the manifold is isometric to $H^{n+1}(-4){\times}{\mathbb{R}}^n$, or, the second order parallel tensor is a constant multiple of the associated metric tensor of $M^{2n+1}$ under certain restriction on k, ${\mu}$. Besides this, we study Ricci soliton on an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}$-nullity distribution. Finally, we characterize such a manifold admitting generalized Ricci soliton.