Convex real projective structures and Weil's local rigidity Theorem

Inkang Kim; Genkai Zhang

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arXiv · 1606.02788

Convex real projective structures and Weil's local rigidity Theorem

Inkang Kim·Genkai Zhang

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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.

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Inkang Kim, Genkai Zhang. 2016-06-09. Convex real projective structures and Weil's local rigidity Theorem. https://arxiv.org/abs/1606.02788

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