Classification of Casorati ideal Legendrian submanifolds in Sasakian space forms II

In Lee et al. (2020) [21], the authors of the present article proved two optimal inequalities delta(C)(n - 1) and (delta(C)) over cap (n - 1) of n-dimensional Legendrian submanifolds in Sasakian space forms and identified the classes of those submanifolds for which the equality cases of both inequalities hold. The aim of this paper is to generalize these results to the case of generalized Casorati curvatures delta(C)(r; n - 1) and (delta(C)) over cap (r; n - 1), which are fundamental extrinsic invariants of Riemannian submanifolds originally introduced by Decu et al. (2008) [14] as a natural generalization of delta(C)(n - 1) and (delta(C)) over cap (n - 1), where ris any real number such that 0 < r < n(n - 1) or r > n(n - 1), respectively. We also provide examples of submanifolds that are ideal for any given r. (c) 2021 Elsevier B.V. All rights reserved.