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It's my first post.

Consider Calabi-Yau threefold $M$ and its tangent bundle $TM$. I know $c_1(TM)=0$ means metric on $M$ is a solution of vacuum Einstein equation. Then my question is "are there any geometrical or physical interpretations of $c_2(TM)$ like $c_1(TM)$?".

Especially I want to know the meaning of $c_{2,i}(TM)\equiv\int_M c_2(TM)\wedge w_i=36$ where $w_i(i=1,\cdots,h^{1,1})$ are standard Kähler forms.

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