Convex real projective structures and Weil's local rigidity Theorem

For an $n$-dimensional real hyperbolic manifold $M$, we calculate the Zariski tangent space of a character variety $\chi(\pi_1(M),SL(n+1,\mathbb R)), n>2$ at Fuchisan loci to show that the tangent space consists of cubic forms. Furthermore we prove the Weil's local rigidity theorem for uniforml hyperbolic lattices using real projective structures.