Traces in complex hyperbolic triangle groups

DOI10.1007/s10711-004-1493-0zbMath1115.32015arXivmath/0402153OpenAlexW2041175347MaRDI QIDQ2487747

Anna Pratoussevitch

Publication date: 8 August 2005

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402153

zbMATH Keywords

trace formulascomplex hyperbolic triangle groupscomplex reflectionscomplex hyperbolic geometrywinding numberstriangles in the complex hyperbolic plane

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Differential geometry of symmetric spaces (53C35) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45) Reflection groups, reflection geometries (51F15)

Related Items (17)

Complex hyperbolic \((3,n,\infty )\) triangle groups ⋮ On a family of triangle groups in complex hyperbolic geometry ⋮ A complex hyperbolic Riley slice ⋮ Groups generated by two elliptic elements in \(\text{PU}(2,1)\). ⋮ Redundancy of Triangle Groups in Spherical CR Representations ⋮ Notes on complex hyperbolic triangle groups of type (\(m, n, \infty\)) ⋮ Configurations of flags and representations of surface groups in complex hyperbolic geometry ⋮ Non-arithmetic monodromy of higher hypergeometric functions ⋮ Notes on complex hyperbolic triangle groups ⋮ New nonarithmetic complex hyperbolic lattices. II ⋮ On the type of triangle groups ⋮ The moduli space of complex geodesics in the complex hyperbolic plane ⋮ Complex lines in complex hyperbolic space \({H_{\mathbb{C}}^{2}}\) ⋮ Cone metrics on the sphere and Livné's lattices ⋮ Special elliptic isometries, relative \(\mathrm{SU}(2,1)\)-character varieties, and bendings ⋮ Discreteness of ultra‐parallel complex hyperbolic triangle groups of type [m1,m2,0] ⋮ Complex hyperbolic triangle groups of type [𝑚,𝑚,0;3,3,2]

Cites Work

• Unnamed Item
• The shape invariant of triangles and trigonometry in two-point homogeneous spaces
• Real hyperbolic on the outside, complex hyperbolic on the inside
• Sur le groupe de la géométrie hyperspherique
• Ideal triangle groups, dented tori, and numerical analysis.
• Degenerating the complex hyperbolic ideal triangle groups

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