Atiyah and Todd classes arising from integrable distributions

In this paper, we study the Atiyah class and the Todd class of the DG manifold [Formula presented] corresponding to an integrable distribution [Formula presented], where [Formula presented] or ℂ. We show that these two classes are canonically identical to those of the Lie pair [Formula presented]. As a consequence, the Atiyah class of a complex manifold X is isomorphic to the Atiyah class of the corresponding DG manifold [Formula presented]. Moreover, if X is a compact Kähler manifold, then the Todd class of X is also isomorphic to the Todd class of the corresponding DG manifold [Formula presented].