| As an important topic in the submanifold geometry,the study of C-totally real submanifolds in Sasakian space forms has attracted much attention.In this paper,we mainly study the classification of C-totally real minimal submanifolds with parallel Ricci tensor in Sasakian space form N2n+1(c),and the results focus on the cases n=3,4.Firstly,by using the parallelism of Ricci tensor and the classical de Rham-Wu’s decomposition theorem,we divide the classification problem into several different cases.In particular,if a 4-dimensional C-totally real minimal submanifold in the Sasakian space form N9(c)is Einstein,we show that it must have constant sectional curvature.Secondly,using the self-adjointness of the shape operator,we successfully construct a frame with typical properties at a point,and then skillfully use the Tsinghua principle,the curvature representation of product manifolds and the implicit function theorem,we get the local typical frame field and the local expression corresponding to the shape operator.Finally,after comparing the expression of the above shape operator with the calculation results of the examples we constructed,we use the uniqueness theorem to get the classification results. |
