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Dergiler / International Electronic Journal of Geometry / 2026 / Volume: 19 Issue: 2

Weakly $\eta$-Einstein Almost Cosymplectic $3$-Manifolds

Ji-eun Lee(Chonnam National University, Department of Mathematics)0000-0003-0698-9596
Sayfa
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Yayın Tarihi
2026-10-25
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Yapay Zeka Hızlı Bakış & Çıkarımlar

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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

If the scalar curvature $r$ of a cosymplectic $3$-manifold $M$ is zero, then $M$ is Einstein, weakly Einstein, and flat.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We show that a strictly almost cosympletic $3$-manifold $M$ is weakly $\eta$-Einstein if and only if $M$ is weakly Einstein.
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Temel Bulgular & Veri:On the other hand, a cosympletic $3$-manifold $M$ is weakly $\eta$-Einstein if and only if $M$ is $\eta$-Einstein.
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Sonuç & Katkı:If the scalar curvature $r$ of a cosymplectic $3$-manifold $M$ is zero, then $M$ is Einstein, weakly Einstein, and flat.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Almost cosymplectic manifold · weakly $\eta$-Einstein · weakly Einstein

Abstract

We show that a strictly almost cosympletic $3$-manifold $M$ is weakly $\eta$-Einstein if and only if $M$ is weakly Einstein. On the other hand, a cosympletic $3$-manifold $M$ is weakly $\eta$-Einstein if and only if $M$ is $\eta$-Einstein. If the scalar curvature $r$ of a cosymplectic $3$-manifold $M$ is zero, then $M$ is Einstein, weakly Einstein, and flat.

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Bu Makaleye Atıf Yap

Lee, J. (2026). Weakly $\eta$-Einstein Almost Cosymplectic $3$-Manifolds. International Electronic Journal of Geometry, Volume: 19 Issue: 2. https://doi.org/10.36890/iejg.1721313

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Kaynakça (21)

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