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Curvature homogeneity and ball-homogeneity on almost coK\"{a}hler 3-manifolds

Yaning Wang
대한수학회 (The Korean Mathematical Society)|2019.01|대한수학회보 (Bulletin of the KMS)|제56권 제1호|pp. 253-263|DOI 10.4134/BKMS.b180222

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참고문헌

키워드

Lie groupalmost coK\"{a}hler 3-manifoldball-homogeneitycurvature homogeneityLocally homogeneity
주제분류수학

초록

Let $M$ be a curvature homogeneous or ball-homogeneous non-coK\"{a}hler almost coK\"{a}hler $3$-manifold. In this paper, we prove that $M$ is locally isometric to a unimodular Lie group if and only if the Reeb vector field $\xi$ is an eigenvector field of the Ricci operator. To extend this result, we prove that $M$ is homogeneous if and only if it satisfies $\nabla_\xi h=2f\phi h$, $f\in\mathbb{R}$.

Abstract

Let $M$ be a curvature homogeneous or ball-homogeneous non-coK\"{a}hler almost coK\"{a}hler $3$-manifold. In this paper, we prove that $M$ is locally isometric to a unimodular Lie group if and only if the Reeb vector field $\xi$ is an eigenvector field of the Ricci operator. To extend this result, we prove that $M$ is homogeneous if and only if it satisfies $\nabla_\xi h=2f\phi h$, $f\in\mathbb{R}$.

참고문헌 (21)

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