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 invariantδ_M and the squared mean curvature are given. The equality cases are also discussed.

We study projective curvature tensor in 𝐾-contact and Sasakian manifolds. We prove that (1) if a 𝐾-contact manifold is quasi projectively flat then it is Einstein and (2) a 𝐾-contact manifold is 𝜉-projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a 𝐾-contact manifold to be quasi projectively flat and 𝜑-projectively flat are obtained. We also prove that for a $(2n+1)$-dimensional Sasakian manifold the conditions of being quasi projectively flat, 𝜑-projectively flat and locally isometric to the unit sphere $S^{2n+1}(1)$ are equivalent. Finally, we prove that a compact 𝜑-projectively flat 𝐾-contact manifold with regular contact vector field is a principal $S^1$-bundle over an almost Kaehler space of constant holomorphic sectional curvature 4.