Slant Immersions of Complex Space Forms and Chen's Inequality

Slant submanifolds of quaternionic space forms

“…From Theorem 5.1 and Lemma 5.3, using the same techniques as in [19], we can state now the following result. Proof.…”

“…The existence of Kählerian slant submanifolds of smallest possible codimension in complex space forms, having unfull first normal bundle, has been investigated in [19]. Next we'll study this problem in the context of slant submanifolds in quaternionic space forms.…”

Some inequalities for submanifolds in a Riemannian manifold of nearly quasi-constant curvature

“…which together with (8) gives (12). The equality case of (12) at a point p ∈ M n holds if and only if we have equality in (17).…”

“…According to Chen's cornerstone work [3], one of the most important problems in submanifold theory is to establish simple relationships between the main extrinsic invariants and the main intrinsic invariants of submanifolds. The basic relationships discovered until now are inequalities and the study of this topic has attracted a lot of attention during the last two decades [5,8,9,[11][12][13][14][15][17][18][19][20][21][22][23].…”