Second variation for L-minimal Legendrian submanifolds in pseudo-Sasakian manifolds

Abstract

In this paper we provide a second variation formula for L-minimal Lagrangian submanifolds in a pseudo-Sasakian manifold. We apply it to the case of Lorentzian-Sasakian manifolds and relate the L-stability of L-minimal Legendrians in a Sasakian M to their L-stability in an associated Lorentzian-Sasakian structure on M.

15 pages; Corrections in the introduction, in Prop 3.3 and 3.7, deleted section 3.3. Final version up to minor aesthetic changes