Minimal Legendrian submanifolds in Sasakian space forms with C-parallel second fundamental form

It is known that Cheng-He-Hu [3] gave a complete classification of the n-dimensional C -totally real (or equivalently, Legendrian) minimal submanifolds in the (2n +1) -dimensional Sasakian space form N2n+1(c) with constant sectional curvature. According to this classification and the proof therein, such minimal Legendrian submanifolds are all of C -parallel second fundamental form. The purpose of this paper is to extend the above result partly, and as the main results, we classify all the minimal Legendrian submanifolds in N2n+1(c) with C-parallel second fundamental form in cases n = 2, 3, 4. (c) 2023 Elsevier B.V. All rights reserved.