Abstract
In this article, we discuss the de Rham cohomology class for bislant submanifolds in nearly trans-Sasakian manifolds. Moreover, we give a classification of warped product bislant submanifolds in nearly trans-Sasakian manifolds with some nontrivial examples in the support. Next, it is of great interest to prove that there does not exist any doubly warped product bislant submanifolds other than warped product bislant submanifolds in nearly trans-Sasakian manifolds. Some immediate consequences are also obtained.
Highlights
Introduction and MotivationsThe most inventive topic in the field of differential geometry currently is the theory of warped product manifolds
Due to the important roles of the warped product in mathematical physics and geometry, it has become the most active and interesting topic for researchers, and many nice results are available in the literature
Chen [4, 5] initiates the concept of warped product submanifolds by proving the nonexistence result of warped product CR-submanifolds of type N ⊥ × f N T in Kähler manifolds, where N ⊥ and N T are anti-invariant and invariant submanifolds, respectively
Summary
The most inventive topic in the field of differential geometry currently is the theory of warped product manifolds. Chen [4, 5] initiates the concept of warped product submanifolds by proving the nonexistence result of warped product CR-submanifolds of type N ⊥ × f N T in Kähler manifolds, where N ⊥ and N T are anti-invariant and invariant submanifolds, respectively He considers warped product CR-submanifolds of type N T × f N ⊥ and gives an inequality involving a warping function f and the squared norm of the second fundamental form khk. The warped product bislant submanifolds in nearly trans-Sasakian manifolds is studied by Siddiqui et al in [1] They obtain several inequalities for the squared norm of the second fundamental form in terms of a warping function f. We investigate the existence of doubly warped products in the same ambient
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