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

TL;DR

This paper derives a second variation formula for L-minimal Legendrian submanifolds in pseudo-Sasakian manifolds and explores their stability in Lorentzian-Sasakian structures.

Contribution

It introduces a second variation formula for L-minimal Legendrians and links their stability properties across different geometric structures.

Findings

Derived a second variation formula for L-minimal Legendrians.

Established a relationship between stability in Sasakian and Lorentzian-Sasakian manifolds.

Applied the formula to Lorentzian-Sasakian cases.

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.