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1. CMB 2011 (vol 55 pp. 329)
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 group Categories:51M10, 32M15, 53C55, 53C35 |
2. CMB 2010 (vol 53 pp. 412)
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 metrics Categories: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 |
4. CMB 1999 (vol 42 pp. 486)
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 |
5. CMB 1997 (vol 40 pp. 204)
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 |