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Rigidity and deformation spaces of strictly convex real projective structures on compact manifolds. (English) Zbl 1076.53053
The author shows that two strictly convex, compact real projective manifolds are projectively equivalent, provided they have the same marked length spectrum with respect to the Hilbert distance.
As in the case of $$\text{CAT}(-1)$$ spaces a central idea is, to study the cross ratio on the ideal boundary of the universal covering.

##### MSC:
 53C24 Rigidity results 58D27 Moduli problems for differential geometric structures 53B10 Projective connections
##### Keywords:
marked length spectrum; rigidity; real projective manifolds
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