Second variational formula and the stability of legendrian minimal submanifolds in sasakian manifolds

In this paper, we investigate compact Legendrian submanifolds L in Sasakian manifolds M, which have extremal volume under Legendrian deformations. We call such a submanifold L-minimal Legendrian submanifold. We derive the second variational for-mula for the volume of L under Legendrian deformations in M. Applying this formula, we investigate the stability of L-minimal Legendrian curves in Sasakian space forms, and show the L-instability of L-minimal Legendrian submanifolds in S²ⁿ¹⁺¹ (1). Moreover, we give a construction of L-minimal Legendrian submanifolds in R²ⁿ⁺¹(-3).