Czechoslovak Mathematical Journal, Vol. 67, No. 1, pp. 73-86, 2017
Minimal Reeb vector fields on almost Kenmotsu manifolds
Received July 13, 2015. First published February 24, 2017.
Abstract: A necessary and sufficient condition for the Reeb vector field of a three dimensional non-Kenmotsu almost Kenmotsu manifold to be minimal is obtained. Using this result, we obtain some classifications of some types of $(k,\mu,\nu)$-almost Kenmotsu manifolds. Also, we give some characterizations of the minimality of the Reeb vector fields of $(k,\mu,\nu)$-almost Kenmotsu manifolds. In addition, we prove that the Reeb vector field of an almost Kenmotsu manifold with conformal Reeb foliation is minimal.
Keywords: almost Kenmotsu manifold; Reeb vector field; minimal vector field; harmonic vector field; Lie group
Affiliations: Yaning Wang, Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, School of Mathematics and Information Sciences, Henan Normal University, No. 46 in Eastern Jianshe Street, Xinxiang 453007, Henan, P. R. China, e-mail: email@example.com