A geometric inequality for warped product semi-slant submanifolds of nearly cosymplectic manifolds

Abstract

Recently, we have shown that there do not exist the warped product semi-slant submanifolds of cosymplectic manifolds [10]. As nearly cosymplectic structure generalizes cosymplectic ones same as nearly Kaehler generalizes Kaehler structure in almost Hermitian setting. It is interesting that the warped product semi-slant submanifolds exist in nearly cosymplectic case while in case of cosymplectic do not exist. In the beginning, we prove some preparatory results and finally we obtain an inequality such as $\|h\|^2 \geq 4q\csc^2\theta\{1+\frac{1}{9}\cos^2\theta\}\|\nabla \ln f\|^2$ in terms of intrinsic and extrinsic invariants. The equality case is also considered.