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

Abstract

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.