Abstract
We classify the polar actions on the complex hyperbolic plane \({\mathbb{C} H^2}\) up to orbit equivalence. Apart from the trivial and transitive polar actions, there are five polar actions of cohomogeneity 1 and four polar actions of cohomogeneity 2.
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Berndt J., Díaz-Ramos J.C.: Real hypersurfaces with constant principal curvatures in the complex hyperbolic plane. Proc. Am. Math. Soc. 135, 3349–3357 (2007)
Berndt J., Tamaru H.: Cohomogeneity one actions on noncompact symmetric spaces of rank one. Trans. Am. Math. Soc. 359, 3425–3438 (2007)
Berndt, J., Díaz-Ramos, J.C.: Homogeneous polar foliations in complex hyperbolic spaces. Comm. Anal. Geom. (to appear)
Berndt, J., Tamaru, H.: Cohomogeneity one actions on symmetric spaces of noncompact type. J. Reine Angew. Math. (to appear)
Berndt, J., Tricerri, F., Vanhecke, L.: Generalized Heisenberg groups and Damek-Ricci harmonic spaces. Lecture Notes in Mathematics, vol. 1598. Springer, Berlin (1995)
Berndt J., Díaz-Ramos J.C., Tamaru H.: Hyperpolar homogeneous foliations on symmetric spaces of noncompact type. J. Differ. Geom. 86, 191–235 (2010)
Díaz-Ramos J.C., Kollross A.: Polar actions with a fixed point. Differ. Geom. Appl. 29, 20–25 (2011)
Kollross A.: Polar actions on symmetric spaces. J. Differ. Geom. 77, 425–482 (2007)
Kollross A.: Low cohomogeneity and polar actions on exceptional compact Lie groups. Transform. Groups 14, 387–415 (2009)
Mostow G.D.: On maximal subgroups of real Lie groups. Ann. Math. 74(2), 503–517 (1961)
Podestà à F., Thorbergsson G.: Polar actions on rank-one symmetric spaces. J. Differ. Geom. 53, 131–175 (1999)
Sakai, T., Riemannian geometry, Translations of Mathematical Monographs, vol. 149. American Mathematical Society, Providence (1996)
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Berndt, J., Díaz-Ramos, J.C. Polar actions on the complex hyperbolic plane. Ann Glob Anal Geom 43, 99–106 (2013). https://doi.org/10.1007/s10455-012-9335-z
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DOI: https://doi.org/10.1007/s10455-012-9335-z