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 submanifolds immersed in a manifold with quarter symmetric connection. (English) Zbl 0982.53016
Let M n+1 be a C -manifoldd with a quarter symmetric metric connection ˙ in the sense of R. S. Mishra and S. N. Pandey [Tensor 34, 1-7 (1980; Zbl 0451.53017)]. It is proved that the connection induced on a hypersurface M n (as well as on a submanifold M n-1 of codimension 2) of such an M n+1 is also quarter symmetric. The hypersurface M n (resp. the submanifold M n-1 ) will be totally umbilic with respect to ˙ if and only if it is totally umbilic with respert to . The Gauss, Weingarten and Codazzi equations are deduced.
53B25Local submanifolds
53B05Linear and affine connections