Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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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.

Reeb flow symmetry on almost cosymplectic three-manifolds

Jong Taek Cho

Chonnam National University

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.

Keywords: almost cosymplectic three-manifold, Reeb flow, Lie group

MSC numbers: 53C21, 53C25, 53C30