zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Classical geometries defined by exterior differential systems on higher frame bundles. (English) Zbl 0672.53035
Let d be the exterior differentiation operator and I a closed differential ideal (dI$\subseteq I)$ over a finite dimensional differentiable manifold, generated by sets of q-forms $\omega\sb q$ $(q=1,2,...)$. An exterior differential system for a geometry generally is a closed differential ideal. The differential geometry of I is essentially reflected in the properties of the generators of I and in the structure equations. In the present paper, the authors study exterior differential ideals and sets of invariant generators for a number of four-dimensional Riemannian conformal and projective geometries determined as sub-bundles of higher frame bundles over the base M. The final section contains some results on the Einstein-Maxwell ideals. The method consists of establishing exterior differential systems for the geometries under consideration, using canonical basic frames. For that purpose, the authors calculate the Cartan characters and the genus g (the maximum dimension of the regular integral manifolds of I).
Reviewer: C.Apreutesei

58A15Exterior differential systems (Cartan theory)
Full Text: DOI