Convex real projective structures and Weil's local rigidity Theorem

Abstract

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.

13 pages. arXiv admin note: substantial text overlap with arXiv:1312.1965

References in corpus (1)

• Eichler-Shimura isomorphism for complex hyperbolic lattices