Characterizing Inequalities for Biwarped Product Submanifolds of Sasakian Space Forms

The biwarped product submanifolds generalize the class of product submanifolds and are particular case of multiply warped product submanifolds. The present paper studies the biwarped product submanifolds of the type ST×ψ1S⊥×ψ2Sθ in Sasakian space forms S¯c, where ST, S⊥, and Sθ are the invariant, anti-invariant, and pointwise slant submanifolds of S¯c. Some characterizing inequalities for the existence of such type of submanifolds are proved; besides these inequalities, we also estimated the norm of the second fundamental form.