Classification of Casorati ideal Legendrian submanifolds in Sasakian space forms II

• DOI: 10.1016/j.geomphys.2021.104410
• Publication Date: 2021-10-22T22:07:04Z
• Authors: Chul Woo Lee; Jae Won Lee; Gabriel-Eduard Vîlcu
• Keywords: 0101 mathematics; 01 natural sciences

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 2 n + 1 ( c ) of constant ϕ -sectional curvature c , we have two sharp inequalities relating some basic extrinsic and intrinsic invariants of the immersion, namely the ϕ -sectional curvature, the normalized scalar curvature, the mean curvature and the δ -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.