zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Discreteness criteria for subgroups in complex hyperbolic space. (English) Zbl 1009.32016

The authors study discreteness criteria for subgroups of U(1,n;) in complex hyperbolic space H n .

The main result in this paper is as follows: A nonelementary subgroup G of U(1,n;) in complex hyperbolic space H n with Condition A is discrete if and only if every two generator subgroup is discrete.

Here we say that G satisfies Condition A provided that G has no sequence {g j } of distinct elements of finite order such that Card(fix(g j ))= in H n and g j I as j.

They also prove that if a nonelementary subgroup G of U(1,n;) contains a sequence {g j } of distinct elements with Card(fix(g j )H n ) and g j I as j, then G contains a non-discrete, nonelementary two generator subgroup.

MSC:
32Q45Hyperbolic and Kobayashi hyperbolic manifolds
32M99Complex spaces with a group of automorphisms
22E99Lie groups