On equivalence of deforming Lie subalgebroids and deforming coisotropic submanifolds

Results on deformations of coisotropic submanifolds and Lie subalgebroids are obtained separately. Due to the close connection between these two objects, in this paper, we attempt to classify the relations between their deformation results. Under the correspondence (a Lie subalgebroid E of A) ↦ (the coisotropic submanifold E⊥ of A∗), two deformation results turn out to be equivalent. However, under the picture (a coisotropic submanifold S of M) ↦ (the Lie subalgebroid N∗S of T∗M), difference in certain regularity conditions emerges.