A basic inequality for submanifolds in a cosymplectic space form

Abstract

For submanifolds tangent to the structure vector field in cosymplectic space forms, we establish a basic inequality between the main intrinsic invariants of the submanifold, namely, its sectional curvature and scalar curvature on one side; and its main extrinsic invariant, namely, squared mean curvature on the other side. Some applications, including inequalities between the intrinsic invariant δM and the squared mean curvature, are given. The equality cases are also discussed.