Changes

</math>

</math>

by additivity of the total Chern class this yields <math>c(T\mathbb{P}^n) = c(TM)(1+(n+1)\omega)</math>, where <math>\omega</math> is a generator of the cohomology ring <math>H^*(\mathbb P^n;\mathbb C)</math>. But this implies that  

by additivity of the total Chern class this yields <math>c(T\mathbb{P}^n) = c(TM)(1+(n+1)\omega)</math>, where <math>\omega</math> is the hyperplane class, a generator of the cohomology ring <math>H^*(\mathbb P^n;\mathbb C)</math>. But this implies that  

::<math>

::<math>