Article

The Fischer-Marsden conjecture on almost Kenmotsu manifolds

Published in: Quaestiones Mathematicae
Volume 43, issue 1, 2020 , pages: 25–33
DOI: 10.2989/16073606.2018.1533499
Author(s): U.C. DeDepartment of Pure Mathematics, India, Krishanu MandalDepartment of Mathematics, K.K. Das College, India

Abstract

The purpose of this paper is to investigate the Fischer-Marsden conjecture on almost Kenmotsu manifolds. First, we prove that if a three-dimensional non-Kenmotsu (k, µ)-almost Kenmotsu manifold satisfies the Fischer-Marsden conjecture, then the manifold is locally isometric to the product space ℍ2(−4) × ℝ. Further, we prove that if the metric of a complete almost Kenmotsu manifold with conformal Reeb foliation satisfies the Fischer-Marsden conjecture, then the manifold is Einstein provided the scalar curvature r ≠ −2n(2n + 1).

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