By using new algebraic techniques, two Casorati inequalities are established for submanifolds in a Riemannian manifold of quasi-constant curvature with a semi-symmetric metric connection, which generalize inequalities obtained by Lee et al. J. Inequal. Appl. 2014, 2014, 327.

In this article, we obtain sharp estimate of the Ricci curvature of quaternion slant, bi-slant and semi-slant submanifolds in a quaternion space form, in terms of the squared mean curvature.

Let A be a domain of the boundary of a strictly pseudoconvex domain Ω of Cn and M a smooth, closed, maximally complex submanifold of A. We find a subdomain à of Ω, depending only on Ω and A, and a complex variety W ⊂ à such that bW ∩A = M . Moreover, a generalization to analytic sets of depth at least 4 is given.

We study semi-Riemannian submanifolds of arbitrary codimension in a Lie group [Formula: see text] equipped with bi-invariant metric. In particular, we show that, if the normal bundle is closed under bracket, then any Jacobi operator equals square associated invariant shape text]. This permits to understand curvature adaptedness geometrically, terms left translations. For example, case where Rie...