arXiv subjects
Publications and source records attributed to Jeong-Sik Kim.
We find the index of $\widetilde{\nabla}$-quasi-conformally symmetric and $\widetilde{\nabla}$-concircularly symmetric semi-Riemannian manifolds, where $\widetilde{\nabla}$ is metric connection.
We obtain certain inequalities involving several intrinsic invariants namely scalar curvature, Ricci curvature and $k$-Ricci curvature, and main extrinsic invariant namely squared mean curvature for submanifolds in a locally conformal almost cosymplectic manifold with pointwise constant $% ϕ$-sectional curvature. Applying these inequalities we obtain several inequalities for slant, invariant, anti-invariant and {\em CR}-submanifolds. The equality cases are also discussed.
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 $δ_{M}$ and the squared mean curvature are given. The equality cases are also discussed
Certain basic inequalities between intrinsic and extrinsic invariants for a submanifold in a (k, m)-contact space form are obtained. As applications we get some results for invariant submanifolds in a (k,m)-contact space form.