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Dergiler / International Electronic Journal of Geometry / 2024 / Volume: 17 Issue: 2

On Ricci Recurrent Almost Kenmotsu $3$-manifolds

Ji-eun Lee(NATIONAL DEFENSE UNIVERSITY, NATIONAL DEFENCE AND SECURITY INSTITUTE)0000-0003-0698-9596
Sayfa
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Yayın Tarihi
2024-10-27
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Thus, an almost Kenmotsu $3$-manifold is $\varphi$-Ricci symmetric if and only if it has dominantly $\eta$-parallel Ricci operator.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we prove first that for an almost Kenmotsu $3$-manifold satisfying $\xi (tr \, h^2)=0$, its Ricci operator is recurrent if and only if the manifold is locally symmetric.
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Temel Bulgular & Veri:Next, we show that $\varphi$-Ricci symmetry and $\varphi$-Ricci recurrence are equivalent conditions in almost Kenmotsu $3$-manifolds.
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Sonuç & Katkı:Thus, an almost Kenmotsu $3$-manifold is $\varphi$-Ricci symmetric if and only if it has dominantly $\eta$-parallel Ricci operator.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Almost Kenmotsu manifold · local symmetry · Ricci recurrent

Abstract

In this paper, we prove first that for an almost Kenmotsu $3$-manifold satisfying $\xi (tr \, h^2)=0$, its Ricci operator is recurrent if and only if the manifold is locally symmetric. Next, we show that $\varphi$-Ricci symmetry and $\varphi$-Ricci recurrence are equivalent conditions in almost Kenmotsu $3$-manifolds. Thus, an almost Kenmotsu $3$-manifold is $\varphi$-Ricci symmetric if and only if it has dominantly $\eta$-parallel Ricci operator.

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Bu Makaleye Atıf Yap

Lee, J. (2024). On Ricci Recurrent Almost Kenmotsu $3$-manifolds. International Electronic Journal of Geometry, Volume: 17 Issue: 2. https://doi.org/10.36890/iejg.1407888

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Kaynakça (17)

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