Another class of warped product submanifolds of Kenmotsu manifolds

Characterization theorems on warped product semi-slant submanifolds in Kenmotsu manifolds

“…The third term of right hand side in above equation is identically zero by using (23) (i). Thus, using (25) in first term and Lemma 4.3 (ii) in the second term, we get first part of the lemma. Again from using (19), we arrive at…”

Another inequality for skew CR-warped products in Kenmotsu manifolds

“…2. Similarly, if dim(M ⊥ ) = 0 in a contact skew CR-warped product, then it will change into a warped product semi-slant submanifold of the form M = M θ × f M T studied in [36]. In this case,Theorem 4.2 of [36] is a particular case of Theorem 3.5 as follows:…”

Bi-warped product submanifolds of Kenmotsu manifolds and their applications

“…(1) If we consider m 2 = 0 in Theorem 6, then the bi-warped product changes into a semi-slant warped product of the form M θ × f1 M T studied in [23]. Hence, the statement of Theorem 6 can be stated as: (2) On the other hand, if m 1 = 0 in Theorem 6, then the bi-warped product…”