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)
The Hunter-Saxton equation describes the geodesic flow on a sphere. (English) Zbl 1125.35085
Author’s summary: The Hunter-Saxton equation is the Euler equation for the geodesic flow on the quotient space Rot(𝕊)𝒟(𝕊) of the infinite-dimensional group 𝒟(𝕊) of orientation-preserving diffeomorphisms of the unit circle 𝕊 modulo the subgroup of rotations Rot(𝕊) equipped with the H ˙ 1 right-invariant metric. We establish several properties of the Riemannian manifold Rot(𝕊)𝒟(𝕊): it has constant curvature equal to 1, the Riemannian exponential map provides global normal coordinates, and there exists a unique length-minimizing geodesic joining any two points of the space. Moreover, we give explicit formulas for the Jacobi fields, we prove that the diameter of the manifold is exactly π 2, and we give exact estimates for how fast the geodesics spread apart. At the end, these results are given a geometric and intuitive understanding when an isometry from Rot(𝕊)𝒟(𝕊) to an open subset of an L 2 -sphere is constructed.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
58B20Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds