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Questions about Kähler manifolds and Kähler metrics.
3
votes
2
answers
501
views
Vector bundle over compact complex manifold which is not holomorphic?
A vector bundle over a complex manifold is said to be holomorphic if its trivialization maps are biholomorphic maps. What is a "natural" example example of a vector bundle over compact complex manifol …
25
votes
1
answer
699
views
The de Rham complex of the octonionic projective spaces
The complex projective space $\mathbb{CP}^n$ is a complex manifold, and hence its de Rham complex carries a representation of the complex numbers in the form of its complex structure. The quaternionic …