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1. CMB 2011 (vol 55 pp. 329)

Kamiya, Shigeyasu; Parker, John R.; Thompson, James M.
 Non-Discrete Complex Hyperbolic Triangle Groups of Type $(n,n, \infty;k)$ A complex hyperbolic triangle group is a group generated by three involutions fixing complex lines in complex hyperbolic space. Our purpose in this paper is to improve a previous result and to discuss discreteness of complex hyperbolic triangle groups of type $(n,n,\infty;k)$. Keywords:complex hyperbolic triangle groupCategories:51M10, 32M15, 53C55, 53C35

2. CMB 2010 (vol 53 pp. 412)

Calvaruso, G.
 Einstein-Like Lorentz Metrics and Three-Dimensional Curvature Homogeneity of Order One We completely classify three-dimensional Lorentz manifolds, curvature homogeneous up to order one, equipped with Einstein-like metrics. New examples arise with respect to both homogeneous examples and three-dimensional Lorentz manifolds admitting a degenerate parallel null line field. Keywords:Lorentz manifolds, curvature homogeneity, Einstein-like metricsCategories:53C50, 53C20, 53C30

3. CMB 2000 (vol 43 pp. 74)

 Geometric Meaning of Isoparametric Hypersurfaces in a Real Space Form We shall provide a characterization of all isoparametric hypersurfaces $M$'s in a real space form $\tilde{M}(c)$ by observing the extrinsic Wshape of geodesics of $M$ in the ambient manifold $\tilde{M}(c)$. Categories:53C35, 53C20, 53C22
 Spherical Functions on $\SO_0(p,q)/\SO(p)\times \SO(q)$ An integral formula is derived for the spherical functions on the symmetric space $G/K=\break \SO_0(p,q)/\SO(p)\times \SO(q)$. This formula allows us to state some results about the analytic continuation of the spherical functions to a tubular neighbourhood of the subalgebra $\a$ of the abelian part in the decomposition $G=KAK$. The corresponding result is then obtained for the heat kernel of the symmetric space $\SO_0(p,q)/\SO (p)\times\SO (q)$ using the Plancherel formula. In the Conclusion, we discuss how this analytic continuation can be a helpful tool to study the growth of the heat kernel. Categories:33C55, 17B20, 53C35
 The $\eta$-invariants of cusped hyperbolic $3$-manifolds In this paper, we define the $\eta$-invariant for a cusped hyperbolic $3$-manifold and discuss some of its applications. Such an invariant detects the chirality of a hyperbolic knot or link and can be used to distinguish many links with homeomorphic complements. Categories:57M50, 53C30, 58G25