A basic inequality for submanifolds in locally conformal almost cosymplectic manifolds

Abstract

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