A class of warped product submanifolds of Kenmotsu manifolds

In 2018 Naghi et al. studied warped product skew CR-submanifold of the form M = M1×f M⊥ of a Kenmotsu manifold M¯ throughout the paper , where M1 = MT ×Mθ and MT , M⊥, Mθ represents invariant, antiinvariant, proper slant submanifold of M¯ . Next, in 2019 Hui et al. studied another class of warped product skew CR-submanifold of the form M = M2 ×f MT of M¯ , where M2 = M⊥ × Mθ . The present paper deals with the study of a class of warped product submanifold of the form M = M3 ×f Mθ of M¯ , where M3 = MT × M⊥ and MT , M⊥, Mθ represents invariant, antiinvariant and proper pointwise slant submanifold of M¯ . A characterization is given on the existence of such warped product submanifolds which generalizes the characterization of warped product contact CR-submanifolds of the form M⊥ ×f MT , studied by Uddin et al. in 2017 and also generalizes the characterization of warped product semi-slant submanifolds of the form MT ×f Mθ , studied by Uddin in the same year. Beside that some inequalities on the squared norm of the second fundamental form are obtained which are also generalizations of the inequalities obtained in the just above two mentioned papers respectively.