In the present work, we consider two types of bi-warped product submanifolds, M=MT×f1M⊥×f2Mϕ and ... more In the present work, we consider two types of bi-warped product submanifolds, M=MT×f1M⊥×f2Mϕ and M=Mϕ×f1MT×f2M⊥, in nearly trans-Sasakian manifolds and construct inequalities for the squared norm of the second fundamental form. The main results here are a generalization of several previous results. We also design some applications, in view of mathematical physics, and obtain relations between the second fundamental form and the Dirichlet energy. The relationship between the eigenvalues and the second fundamental form is also established.
In the present paper, we establish two general sharp inequalities for the squared norm of second ... more In the present paper, we establish two general sharp inequalities for the squared norm of second fundamental form for mixed totally geodesic warped product pseudo-slant submanifolds of the form M? xf M? and M? xf M?, in a nearly Kenmotsu f-manifold M, which include the squared norm of the warping function and slant angle. Also, equality cases are verified. We proved that some previous results are trivial from our results. Moreover, we generalized the inequality theorems [3] and [26] from our derived results.
In the present work, we consider two types of bi-warped product submanifolds, M=MT×f1M⊥×f2Mϕ and ... more In the present work, we consider two types of bi-warped product submanifolds, M=MT×f1M⊥×f2Mϕ and M=Mϕ×f1MT×f2M⊥, in nearly trans-Sasakian manifolds and construct inequalities for the squared norm of the second fundamental form. The main results here are a generalization of several previous results. We also design some applications, in view of mathematical physics, and obtain relations between the second fundamental form and the Dirichlet energy. The relationship between the eigenvalues and the second fundamental form is also established.
In the present paper, we establish two general sharp inequalities for the squared norm of second ... more In the present paper, we establish two general sharp inequalities for the squared norm of second fundamental form for mixed totally geodesic warped product pseudo-slant submanifolds of the form M? xf M? and M? xf M?, in a nearly Kenmotsu f-manifold M, which include the squared norm of the warping function and slant angle. Also, equality cases are verified. We proved that some previous results are trivial from our results. Moreover, we generalized the inequality theorems [3] and [26] from our derived results.
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Papers by Ali Alkhaldi