# geometrical or physical interpretation of second Chern classes of Calabi-Yau threefold

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.