Rigidity and deformation spaces of strictly convex real projective structures on compact manifolds. (English) Zbl 1076.53053

Kim, Inkang

J. Differ. Geom. 58, No. 2, 189-218 (2001).

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.

Reviewer: Gerhard Knieper (Bochum)

MSC:

53C24	Rigidity results
58D27	Moduli problems for differential geometric structures
53B10	Projective connections

Keywords:

marked length spectrum; rigidity; real projective manifolds