There are three questions:
- Please let me know your proof of the following theorem:
If $CP^3$ can be immersed in $R^8$ with an Euler class $W_{2}(\nu)$ for the normal bundle of $CP^3$ respect to $R^8$ then $$\int_{CP^3} \!W_{{2}} \left( \nu \right) c^2$$ is divisible by 3.
Where $c$ is the cohomological generator of $CP^3$.
- What is the exact value of the integral
$$\int_{CP^3} \!W_{{2}} \left( \nu \right) c^2$$
- It is possible to have an immersion of $CP^3$ in $R^8$?
Many thanks.