A basic inequality for submanifolds in locally conformal almost cosymplectic manifolds

摘要

For submanifolds tangent to the structure vector field in locally conformal almost cosymplectic manifolds of pointwise constant φ-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 invariant δ_M and the squared mean curvature are given. The equality cases are also discussed.