Answer by Peter Michor for Diffeomorphisms on a real manifold whose...
I guess that you mean: $TM$ carries an almost complex structure $J:TM\to TM$ with $J^2=-1$. It is integrable to complex structure iff the Froelicher-Nijenhuis bracket $[J,J]$ vanishes.First question:...
View ArticleDiffeomorphisms on a real manifold whose derivative are holomorphic maps on...
Edit: According to the answers to the linked MSE question and the comment of Holonomia, I understand that the answer to the second question is that " Every tangent bundles is a complex manifold".Let...
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