Kodai Mathematical Journal
Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991
Minimal Reeb vector fields on almost cosymplectic manifolds
Domenico Perrone
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2013 年 36 巻 2 号 p. 258-274

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We show that the Reeb vector field of an almost cosymplectic three-manifold is minimal if and only if it is an eigenvector of the Ricci operator. Then, we show that Reeb vector field ξ of an almost cosymplectic three-manifold M is minimal if and only if M is (κ, μ, ν)-space on an open dense subset. After, using the notion of strongly normal unit vector field introduced in [8], we study the minimality of ξ for an almost cosymplectic (2n + 1)-manifold. Finally, we classify a special class of almost cosymplectic three-manifold whose Reeb vector field is minimal.
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© 2013 Department of Mathematics, Tokyo Institute of Technology
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