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)
On some pseudosymmetry type curvature condition. (English) Zbl 1047.53040
In several papers the authors and some of their collaborators published already a series of results concerning pseudo-Riemannian manifolds satisfying some “pseudo-symmetry” curvature condition. In this paper they continue this research. Let $(M, g)$ be a pseudo-Riemannian manifold, $R$ its curvature tensor and $C$ the corresponding Weyl tensor. They study manifolds $(M,g)$ such that $R\cdot C-C\cdot R$ and the tensor $Q(g,R)$, which they defined in earlier papers, are linearly dependent at any point of $M$. Here $R$ and $C$ act as derivations. Their main result is that such manifolds must be semi-symmetric, i.e. $R\cdot R= 0$, a condition which provided the starting point of their research on this type of conditions. Furthermore, they provide some examples of semi-symmetric warped products which satisfy the relation mentioned above and which illustrate their search for a possible inverse of their main result.

53C50Lorentz manifolds, manifolds with indefinite metrics
53B30Lorentz metrics, indefinite metrics