ABSTRACT
For a CR submanifold of ℂ n , there are two ways to define the tangential Cauchy–Riemann complex and both approaches appear in the literature. The first way is an extrinsic approach that uses the ∂ ¯ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315140445/fbe50be4-2923-45ad-961d-51ed68ffe025/content/inequ819.tif"/> -complex of the ambient ℂ n . The second way is an intrinsic approach that makes no use of the ambient ℂ n and therefore generalizes to abstract CR manifolds. In this chapter, we present both approaches. In the imbedded case, these approaches lead to different tangential Cauchy–Riemann complexes but in Section 8.3, we show they are isomorphic.
