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Questions about Kähler manifolds and Kähler metrics.

2 votes
2 answers
486 views

Are Chern classes always vertical?

Let $c_k \in H^{2k}(M, \mathbb{Z})$ be the $k$-th Chern class of the tangent bundle of a Hermitian manifold $M$. Is $c_k$ necessarily vertical, i.e. $$ c_k = \sum_{i_1,\dots, i_{k}} \alpha_{i_1 \dots …
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