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I came across the book on Cauchy Riemann manifolds, "CR manifolds and tangential Cauchy Riemann complexes". The book does not have a problem section. I would be grateful if anyone recommends some problem books on this topic "Complex manifold" and that would also serve as a supplement to this book.

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    $\begingroup$ Are you looking for problems about CR manifolds, or about complex manifolds? They are very different subjects. $\endgroup$
    – Jack Lee
    Commented Jun 19, 2021 at 20:08
  • $\begingroup$ Either of them would serve the purpose for now but since I would like to use it as a supplement to Albert Boggess's book CR manifolds and tangential Cauchy Riemann complexes I would be a bit biased towards CR manifolds thank you $\endgroup$ Commented Jun 20, 2021 at 3:39

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My book, https://www.jirka.org/scv has a little bit on the topic with exercises, but really only for hypersurfaces. It may be good to go through something like Lee's Smooth Manifolds. Lots of exercises, though on manifolds in general, not CR manifolds specifically. CR manifolds are really just smooth manifolds with a certain structure defined.

Krantz also covers CR manifolds to a certain extent and has lots of exercises. So does D'Angelo. Though, I can't think of an elementary textbook with exercises specifically on CR manifolds.

I learned CR geometry from the Baouendi, Ebenfelt, Rothschild. But no exercises there either.

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