Given an imaginary quadratic extension of , we classify the maximal nonelementary subgroups of the Picard modular group preserving a totally real totally geodesic plane in the complex hyperbolic plane . We prove that these maximal -Fuchsian subgroups are arithmetic, and describe the quaternion algebras from which they arise. For instance, if the radius of the corresponding -circle lies in , then the stabiliser arises from the quaternion algebra . We thus prove the existence of infinitely many orbits of -arithmetic -circles in the hypersphere of .
@article{CML_2018__10_2_75_0, author = {Jouni Parkkonen and Fr\'ed\'eric Paulin}, title = {A classification of $\protect \mathbb{R}${-Fuchsian} subgroups of {Picard} modular groups}, journal = {Confluentes Mathematici}, pages = {75--92}, publisher = {Institut Camille Jordan}, volume = {10}, number = {2}, year = {2018}, doi = {10.5802/cml.51}, mrnumber = {3928225}, language = {en}, url = {https://cml.centre-mersenne.org/articles/10.5802/cml.51/} }
TY - JOUR AU - Jouni Parkkonen AU - Frédéric Paulin TI - A classification of $\protect \mathbb{R}$-Fuchsian subgroups of Picard modular groups JO - Confluentes Mathematici PY - 2018 SP - 75 EP - 92 VL - 10 IS - 2 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.51/ DO - 10.5802/cml.51 LA - en ID - CML_2018__10_2_75_0 ER -
%0 Journal Article %A Jouni Parkkonen %A Frédéric Paulin %T A classification of $\protect \mathbb{R}$-Fuchsian subgroups of Picard modular groups %J Confluentes Mathematici %D 2018 %P 75-92 %V 10 %N 2 %I Institut Camille Jordan %U https://cml.centre-mersenne.org/articles/10.5802/cml.51/ %R 10.5802/cml.51 %G en %F CML_2018__10_2_75_0
Jouni Parkkonen; Frédéric Paulin. A classification of $\protect \mathbb{R}$-Fuchsian subgroups of Picard modular groups. Confluentes Mathematici, Volume 10 (2018) no. 2, pp. 75-92. doi : 10.5802/cml.51. https://cml.centre-mersenne.org/articles/10.5802/cml.51/
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