Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 12 (2019), 440–449 Research Article ISSN: 2008-1898 Journal Homepage: www.isr-publications.com/jnsa Contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly Sasakian structure Amira A. Ishan a,∗ , Meraj Ali Khan b a Department of Mathematics, Taif University, Taif, Kingdom of Saudi Arabia. b Department of Mathematics, University of Tabuk, Kingdom of Saudi Arabia. Abstract This paper studies the contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly Sasakian structure. Some Characterization of the existence of these warped product submanifolds are also obtained. We illustrate that the warping function is a harmonic function under certain conditions. Moreover, a sharp estimate for the squared norm of the second fundamental form is investigated, and the equality case is also discussed. The results obtained in this paper generalize the results that have appeared in [I. Hasegawa, I. Mihai, Geom. Dedicata, 102 (2003), 143–150], [I. Mihai, Geom. Dedicata, 109 (2004), 165–173], and [M. Atc ¸eken, Hacet. J. Math. Stat., 44 (2015), 23–32]. Keywords: Warped products, CR-submanifolds, nearly Sasakian manifolds. 2010 MSC: 53C25, 53C40, 53C42, 53D15. c 2019 All rights reserved. 1. Introduction It is well known that warped products of manifolds play an important role in differential geometry, the theory of relativity and mathematical physics. One of the most important examples of a warped product manifold is the excellent setting to the model space time near black holes or bodies with high gravitational fields [16]. For a recent survey of warped products on Riemannian manifolds, one can consult the reference [14]. The notion of the CR-warped product submanifolds was first introduced by Chen in [12]. Basically, Chen considered the warped product submanifolds of the types N ⊥ × ψ N T and N T × ψ N ⊥ , where N T and N ⊥ are the holomorphic and totally real submanifolds of a Kaehler manifold and showed that the first type of warped product does not exist. Chen obtained some basic results for the second type of warped product submanifolds. He also proved a sharp estimate for the squared norm of the second fun- damental form in terms of the warping function. Hasegawa and Mihai [15] extended the results of Chen [12] in the setting of the Sasakian space forms and obtained a sharp inequality for the squared norm of the second fundamental form in terms of the warping function. A step forward was made by Mihai [21] who ∗ Corresponding author Email addresses: amiraishan@hotmail.com (Amira A. Ishan), meraj79@gmail.com (Meraj Ali Khan) doi: 10.22436/jnsa.012.07.03 Received: 2018-12-01 Revised: 2019-02-14 Accepted: 2019-02-21