Classification of Casorati ideal Legendrian submanifolds in Sasakian space forms

Abstract

In the first part of this paper, using an optimization method on Riemannian submanifolds, we prove that for any Legendrian submanifold of a Sasakian space form (M) over bar (2n+1) Pl(c) of constant phi-sectional curvature c, we have two sharp inequalities relating some basic extrinsic and intrinsic invariants of the immersion, namely the phi-sectional curvature, the normalized scalar curvature, the mean curvature and the delta-Casorati curvatures. In the second part, we classify the family of Casorati ideal Legendrian submanifolds in a Sasakian space form and provide examples supporting the main results of the paper. (C) 2020 Elsevier B.V. All rights reserved.