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)
Einstein solvmanifolds and nilsolitons. (English) Zbl 1186.53058
Gordon, Carolyn S. (ed.) et al., New developments in Lie theory and geometry. Proceedings of the 6th workshop on Lie theory and geometry, Cruz Chica, Córdoba, Argentina, November 13–17, 2007. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4651-3/pbk). Contemporary Mathematics 491, 1-35 (2009).

The only known examples of noncompact homogeneous Riemannian manifolds which admit invariant Einstein metric are simply connected solvable Lie groups with a left invariant Riemannian metric (solvmanifolds). There is a conjecture that these examples exhaust all the possibilities and the conjecture is true up to dimension 5.

The paper gives a detailed report on the present status of the study of Einstein solvmanifolds.

A generalization of Einstein metrics is the notion of Ricci soliton. If S is an Einstein solvmanifolds, then the metric restricted to the submanifold N=[S,S] is a Ricci soliton and conversely, any Ricci soliton left invariant metric on a nilpotent Lie group N (a nilsoliton) can be extended to an Einstein solvmanifold. The problem of classification of Einstein solvmanifolds is equivalent to the classification of Ricci solitons on nilpotent Lie groups.

MSC:
53C25Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C30Homogeneous manifolds (differential geometry)
22E25Nilpotent and solvable Lie groups