Ricci Solitons and Certain Related Metrics on Almost Co-Kaehler Manifolds
DOI:
https://doi.org/10.15407/mag16.04.402Анотація
У статті вивчаються солітони Річчі та узагальнена $m$-квазі-ейнштейнова метрика на майже ко-келеровому многовиду $M$, що задовольняє нуль-умову. Спочатку ми розглядаємо не ко-келерову $(\kappa, \mu)$-майже ко-келерову метрику як солітон Річчі і доводимо, що солітон розширюється з $\lambda=-2n\kappa$, а векторне поле солітона $X$ залишає структурні тензори $\eta,\xi$ and $\varphi$ інваріантними. Даний результат узагальнює Теорему 5.1 з [32]. Побудовано приклад існування солітона Річчі на $M$. Наприкінці ми доводимо що, якщо $M$ це узагальнений $(\kappa, \mu)$-майже ко-келеровий многовид розмірності більшої за 3, такий що $h\neq 0$, то тоді метрика $M$ не може бути узагальненою $m$-квазі-ейнштейнновою метрикою, і це включає результат нещодавно отриманий Вангом [37, Theorem 4.1] як окремий випадок.
Mathematics Subject Classification: 53C25, 53C15, 53D15
Ключові слова:
майже ко-келеровий многовид, солітон Річчі, узагальнена m-квазі-ейнштейнова метрика, розподіл (κ, μ)-обнуленняПосилання
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