Bulletin of the Iranian Mathematical Society https://doi.org/10.1007/s41980-018-0082-1 ORIGINAL PAPER External Geometry of Submanifolds in Conformal Kenmotsu Manifolds Roghayeh Abdi 1 Received: 13 June 2016 / Accepted: 25 November 2017 © Iranian Mathematical Society 2018 Abstract The object of the present paper is to study submanifolds of a conformal Kenmotsu manifold of which the second fundamental form is recurrent, 2-recurrent or generalized 2-recurrent. Finally, we present an example to verify our results. Keywords Conformal Kenmotsu manifold · Recurrent tensor field · Totally geodesic · Totally umbilic Mathematics Subject Classification Primary 53C25; Secondary 53C40 1 Introduction In [8], Kenmotsu defined and studied a new class of almost contact manifolds called Kenmotsu manifolds. It is well-known that Kenmotsu manifolds are warped product spaces. The notion of warped product is very important in differential geometry as well as in physics. For instance, the best relativistic model of Schwarzschild space-time that describes the out space around a massive star or a black hole is given as warped product [4,10]. Let ( M , J , g) be an almost Hermitian manifold of dimension 2n, where J denotes the almost complex structure and g the Hermitian metric. Then ( M , J , g) is called a locally conformal Kaehler manifold if for each point p of M there exists an open neighborhood U of p and a positive function f U on U so that the local metric g U = exp(− f )g |U is Kaehlerian. If U = M , then the manifold ( M , J , g) is said to be a globally conformal Kaehler manifold. The 1-form ω = df is called the Lee form and its metrically equivalent vector field ω ♯ = grad f , where ♯ means the rising of the Communicated by J. H. Eschenburg. B Roghayeh Abdi rabdi@azaruniv.ac.ir 1 Department of Mathematics, Azarbaijan shahid Madani University, Tabriz 53751 71379, Iran 123