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- W4386875657 abstract "For any maximal surface group representation into $mathrm{SO}_0(2,n+1)$, we introduce a non-degenerate scalar product on the the first cohomology group of the surface with values in the associated flat bundle. In particular, it gives rise to a non-degenerate Riemannian metric on the smooth locus of the subset consisting of maximal representations inside the character variety. In the case $n=2$, we carefully study the properties of the Riemannian metric on the maximal connected components, proving that it is compatible with the orbifold structure and finding some totally geodesic sub-varieties. Then, in the general case, we explain when a representation with Zariski closure contained in $mathrm{SO}_0(2,3)$ represents a smooth or orbifold point in the maximal $mathrm{SO}_0(2,n+1)$-character variety and we show that the associated space is totally geodesic for any $nge 3$." @default.
- W4386875657 created "2023-09-20" @default.
- W4386875657 creator A5071832815 @default.
- W4386875657 date "2023-09-17" @default.
- W4386875657 modified "2023-09-27" @default.
- W4386875657 title "Riemannian geometry of maximal surface group representations acting on pseudo-hyperbolic space" @default.
- W4386875657 doi "https://doi.org/10.48550/arxiv.2309.09351" @default.
- W4386875657 hasPublicationYear "2023" @default.
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