On totally geodesic boundaries of hyperbolic $3$-manifolds
نویسندگان
چکیده
منابع مشابه
Geodesic planes in hyperbolic 3-manifolds
In this talk we discuss the possible closures of geodesic planes in a hyperbolic 3-manifold M. When M has finite volume Shah and Ratner (independently) showed that a very strong rigidity phenomenon holds, and in particular such closures are always properly immersed submanifolds of M with finite area. Manifolds with infinite volume, however, are far less understood and are the main subject of th...
متن کاملGeodesic Intersections in Arithmetic Hyperbolic 3-manifolds
It was shown by Chinburg and Reid that there exist closed hyperbolic 3-manifolds in which all closed geodesics are simple. Subsequently, Basmajian and Wolpert showed that almost all quasi-Fuchsian 3-manifolds have all closed geodesics simple and disjoint. The natural conjecture arose that the Chinburg-Reid examples also had disjoint geodesics. Here we show that this conjecture is both almost tr...
متن کاملSmall Hyperbolic 3-Manifolds With Geodesic Boundary
We classify the orientable finite-volume hyperbolic 3-manifolds having nonempty compact totally geodesic boundary and admitting an ideal triangulation with at most four tetrahedra. We also compute the volume of all such manifolds, we describe their canonical Kojima decomposition, and we discuss manifolds having cusps. The manifolds built from one or two tetrahedra were previously known. There a...
متن کاملThe length spectra of arithmetic hyperbolic 3-manifolds and their totally geodesic surfaces
We examine the relationship between the length spectrum and the geometric genus spectrum of an arithmetic hyperbolic 3-orbifold M . In particular we analyze the extent to which the geometry of M is determined by the closed geodesics coming from finite area totally geodesic surfaces. Using techniques from analytic number theory, we address the following problems: Is the commensurability class of...
متن کاملOn deformations of hyperbolic 3–manifolds with geodesic boundary
Let M be a complete finite-volume hyperbolic 3–manifold with compact non-empty geodesic boundary and k toric cusps, and let T be a geometric partially truncated triangulation of M . We show that the variety of solutions of consistency equations for T is a smooth manifold or real dimension 2k near the point representing the unique complete structure on M . As a consequence, the relation between ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Kodai Mathematical Journal
سال: 1992
ISSN: 0386-5991
DOI: 10.2996/kmj/1138039601