Kim, Inkang Marked length rigidity of rank one symmetric spaces and their product. (English) Zbl 0997.53034 Topology 40, No. 6, 1295-1323 (2001). The author proves that if two Zariski dense representations (not necessarily discrete, nor faithful, nor co-finite volume), from a group \(G\) into \(\text{Iso}(X)\) where \(X\) is a rank one symmetric space, have the proportional marked length spectrum, then they are conjugate (Theorem A). As a generalization of this result, in Section 8 the author shows that a Zariski dense representation into the isometry group of the product of rank one symmetric spaces is determined by the marked cross ratio. Reviewer: Neculai Papaghiuc (Iaşi) Cited in 1 ReviewCited in 15 Documents MSC: 53C24 Rigidity results 53C35 Differential geometry of symmetric spaces 53C10 \(G\)-structures Keywords:marked length spectrum; cross ratio; rank-one symmetric space PDF BibTeX XML Cite \textit{I. Kim}, Topology 40, No. 6, 1195--1323 (2001; Zbl 0997.53034) Full Text: DOI arXiv OpenURL