Bull. Korean Math. Soc. 2016; 53(4): 1249-1257
Printed July 31, 2016
https://doi.org/10.4134/BKMS.b150656
Copyright © The Korean Mathematical Society.
Jong Taek Cho
Chonnam National University
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.
Keywords: almost cosymplectic three-manifold, Reeb flow, Lie group
MSC numbers: 53C21, 53C25, 53C30
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