• 제목/요약/키워드: Almost Ricci solitons

검색결과 19건 처리시간 0.021초

*-CONFORMAL RICCI SOLITONS ON ALMOST COKÄHLER MANIFOLDS

  • Tarak Mandal;Avijit Sarkar
    • 대한수학회논문집
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    • 제38권3호
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    • pp.865-880
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    • 2023
  • The main intention of the current paper is to characterize certain properties of *-conformal Ricci solitons on non-coKähler (𝜅, 𝜇)-almost coKähler manifolds. At first, we find that there does not exist *-conformal Ricci soliton if the potential vector field is the Reeb vector field θ. We also prove that the non-coKähler (𝜅, 𝜇)-almost coKähler manifolds admit *-conformal Ricci solitons if the potential vector field is the infinitesimal contact transformation. It is also studied that there does not exist *-conformal gradient Ricci solitons on the said manifolds. An example has been constructed to verify the obtained results.

BETA-ALMOST RICCI SOLITONS ON ALMOST COKÄHLER MANIFOLDS

  • Kar, Debabrata;Majhi, Pradip
    • Korean Journal of Mathematics
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    • 제27권3호
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    • pp.691-705
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    • 2019
  • In the present paper is to classify Beta-almost (${\beta}$-almost) Ricci solitons and ${\beta}$-almost gradient Ricci solitons on almost $CoK{\ddot{a}}hler$ manifolds with ${\xi}$ belongs to ($k,{\mu}$)-nullity distribution. In this paper, we prove that such manifolds with V is contact vector field and $Q{\phi}={\phi}Q$ is ${\eta}$-Einstein and it is steady when the potential vector field is pointwise collinear to the reeb vectoer field. Moreover, we prove that a ($k,{\mu}$)-almost $CoK{\ddot{a}}hler$ manifolds admitting ${\beta}$-almost gradient Ricci solitons is isometric to a sphere.

GRADIENT ALMOST RICCI SOLITONS WITH VANISHING CONDITIONS ON WEYL TENSOR AND BACH TENSOR

  • Co, Jinseok;Hwang, Seungsu
    • 대한수학회지
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    • 제57권2호
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    • pp.539-552
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    • 2020
  • In this paper we consider gradient almost Ricci solitons with weak conditions on Weyl and Bach tensors. We show that a gradient almost Ricci soliton has harmonic Weyl curvature if it has fourth order divergence-free Weyl tensor, or it has divergence-free Bach tensor. Furthermore, if its Weyl tensor is radially flat, we prove such a gradient almost Ricci soliton is locally a warped product with Einstein fibers. Finally, we prove a rigidity result on compact gradient almost Ricci solitons satisfying an integral condition.

RICCI SOLITONS AND RICCI ALMOST SOLITONS ON PARA-KENMOTSU MANIFOLD

  • Patra, Dhriti Sundar
    • 대한수학회보
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    • 제56권5호
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    • pp.1315-1325
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    • 2019
  • The purpose of this article is to study the Ricci solitons and Ricci almost solitons on para-Kenmotsu manifold. First, we prove that if a para-Kenmotsu metric represents a Ricci soliton with the soliton vector field V is contact, then it is Einstein and the soliton is shrinking. Next, we prove that if a ${\eta}$-Einstein para-Kenmotsu metric represents a Ricci soliton, then it is Einstein with constant scalar curvature and the soliton is shrinking. Further, we prove that if a para-Kenmotsu metric represents a gradient Ricci almost soliton, then it is ${\eta}$-Einstein. This result is also hold for Ricci almost soliton if the potential vector field V is pointwise collinear with the Reeb vector field ${\xi}$.

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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    • 제62권4호
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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.

*-Ricci Soliton on (κ < 0, µ)-almost Cosymplectic Manifolds

  • Rani, Savita;Gupta, Ram Shankar
    • Kyungpook Mathematical Journal
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    • 제62권2호
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    • pp.333-345
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    • 2022
  • We study *-Ricci solitons on non-cosymplectic (κ, µ)-acs (almost cosymplectic) manifolds M. We find *-solitons that are steady, and such that both the scalar curvature and the divergence of the potential field is negative. Further, we study concurrent, concircular, torse forming and torqued vector fields on M admitting Ricci and *-Ricci solitons. Also, we provide some examples.

On *-Conformal Ricci Solitons on a Class of Almost Kenmotsu Manifolds

  • Majhi, Pradip;Dey, Dibakar
    • Kyungpook Mathematical Journal
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    • 제61권4호
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    • pp.781-790
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    • 2021
  • The goal of this paper is to characterize a class of almost Kenmotsu manifolds admitting *-conformal Ricci solitons. It is shown that if a (2n + 1)-dimensional (k, µ)'-almost Kenmotsu manifold M admits *-conformal Ricci soliton, then the manifold M is *-Ricci flat and locally isometric to ℍn+1(-4) × ℝn. The result is also verified by an example.

SOLITON FUNCTIONS AND RICCI CURVATURES OF D-HOMOTHETICALLY DEFORMED f-KENMOTSU ALMOST RIEMANN SOLITONS

  • Urmila Biswas;Avijit Sarkar
    • 대한수학회논문집
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    • 제38권4호
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    • pp.1215-1231
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    • 2023
  • The present article contains the study of D-homothetically deformed f-Kenmotsu manifolds. Some fundamental results on the deformed spaces have been deduced. Some basic properties of the Riemannian metric as an inner product on both the original and deformed spaces have been established. Finally, applying the obtained results, soliton functions, Ricci curvatures and scalar curvatures of almost Riemann solitons with several kinds of potential vector fields on the deformed spaces have been characterized.