Abstract: In this paper, we consider the n-dimensional Legendrian submanifolds in the 2n+1-dimensional Sasakian space forms based on the basic formula of submanifolds. First, we obtain an inequality on the second fundamental form and the mean curvature vector of the Legendrian submanifold, and further establish an integral inequality for the n-dimensional compact Legendrian submanifold using the classic K. Yano's formula.

Key words: Sasakian space form, Legendrian submanifold, second fundamental form, mean curvature vector