Strongly homotopy Lie algebras and deformations of calibrated submanifolds

For an element $\Psi$ in the graded vector space $\Omega^*(M, TM)$ of tangent bundle valued forms on a smooth manifold $M$, $\Psi$-submanifold is defined as submanifold $N$ $M$ such that $\Psi_{|N} \in \Omega^*(N, TN)$. The class $\Psi$-submanifolds encompasses calibrated submanifolds, complex submanifolds and all Lie subgroups compact groups. carries natural algebra structure, given by Frolicher-Nijenhuis bracket $[-,- ]^{FN}$. When odd degree with $[ \Psi, \Psi]^{FN} =0$, we associate to strongly homotopy algebra, which governs formal (under certain assumptions) deformations $\Psi$-submanifold, show under assumptions these form analytic variety. As application revisit deformation theory closed $\varphi$-calibrated where $\varphi$ parallel real Riemannian manifold.