In the present paper, we study warped product semi-slant submanifolds of a Kenmotsu manifold. We obtain some results on the existence of such type warped product submanifolds of a Kenmotsu manifold with an example. | Turk J Math 36 (2012) , 319 – 330. ¨ ITAK ˙ c TUB doi: Warped product submanifolds of a Kenmotsu manifold Siraj Uddin∗, Viqar Azam Khan and Khalid Ali Khan Abstract In the present paper, we study warped product semi-slant submanifolds of a Kenmotsu manifold. We obtain some results on the existence of such type warped product submanifolds of a Kenmotsu manifold with an example. Key Words: Warped product, slant submanifold, semi-slant submanifold, Kenmotsu manifold, canonical structure 1. Introduction In [13] S. Tanno classified the connected almost contact metric manifold whose automorphism group has maximum dimension; there are three classes: (a) Homogeneous normal contact Riemannian manifolds with constant φ holomorphic sectional curvature if the sectional curvature of the plane section containing ξ , say C(X, ξ) > 0. (b) Global Riemannian product of a line or a circle and a Kaehlerian manifold with constant holomorphic sectional curvature, C(X, ξ) = 0. (c) A warped product space R ×λ Cn , if C(X, ξ) < 0. Manifolds of class (a) are characterized by some tensor equations, it has a Sasakian structure and manifolds of class (b) are characterized by a tensorial relation admitting a cosymplectic structure. Kenmotsu [7] obtained some tensorial equations to characterize manifolds of class (c). As Kenmotsu manifolds are themselves warped product spaces, it is interesting to study warped product submanifolds in Kenmotsu manifolds. The notion of semi-slant submanifolds of almost Hermitian manifolds were introduced by N. Papaghuic [11]. In the setting of almost contact metric manifolds, semi-slant submanifolds are defined and investigated by J. L. Cabrerizo et al. [4]. In [2] R. L. Bishop and B. O’Neill introduced the notion of warped product manifolds. These manifolds appear in differential geometric studies in a natural way. The study of warped product submanifolds of Kaehler manifolds was introduced by B. Y. Chen [6]. After that, B. Sahin extended .
