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Reeb flow symmetry on almost cosymplectic three-manifolds

Jong Taek Cho
대한수학회 (The Korean Mathematical Society)|2016.07|대한수학회보 (Bulletin of the KMS)|제53권 제4호|pp. 1249-1257

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참고문헌

키워드

Lie groupReeb flowalmost cosymplectic three-manifold
주제분류수학

초록

We prove that the Ricci operator $S$ of an almost cosymplectic three-manifold $M$ is invariant along the Reeb flow, that is, $M$ satisfies $\pounds_\xi S=0$ if and only if $M$ is either cosymplectic or locally isometric to the group $E(1,1)$ of rigid motions of Minkowski 2-space with a left invariant almost cosymplectic structure.

Abstract

We prove that the Ricci operator $S$ of an almost cosymplectic three-manifold $M$ is invariant along the Reeb flow, that is, $M$ satisfies $\pounds_\xi S=0$ if and only if $M$ is either cosymplectic or locally isometric to the group $E(1,1)$ of rigid motions of Minkowski 2-space with a left invariant almost cosymplectic structure.

참고문헌 (14)

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