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)
Semi-slant submanifolds of a Sasakian manifold. (English) Zbl 0944.53028
Let M ˜ be an almost contact metric manifold and (φ,ξ,η,g) its almost contact metric structure [see, e.g., D. E. Blair, Lect. Notes Math. 509, Springer-Verlag (1976; Zbl 0319.53026)]. Let M be a Riemannian manifold isometrically immersed in M ˜, for which the structure vector field ξ is tangent to M. Denote by 𝒟 the orthogonal complement of ξ in TM. For a nonzero vector XT p M, which is not colinear with ξ p , denote by θ(X) the angle between φX and 𝒟 p . The submanifold (the distribution 𝒟) is said to be slant [A. Lotta, Bull. Math. Soc. Roum. 39, 183-198 (1996; Zbl 0885.53058)] if the angle θ(X) is independent of the choice of X𝒟 p and pM. The authors define M to be semi-slant if there exist two orthogonal distributions 𝒟 1 , 𝒟 2 such that TM=𝒟 1 𝒟 2 {ξ}, 𝒟 1 is invariant (φ(𝒟 1 )=𝒟 1 ) and 𝒟 2 is slant. They find necessary and sufficient conditions for M to be semi-slant, and study properties of such submanifolds. Among other things, they study integrability conditions for various distributions involved with the definition of semi-slantness in the case when the ambient manifold is Sasakian. See also recent papers by the same authors.

53C40Global submanifolds (differential geometry)
53D15Almost contact and almost symplectic manifolds
53C25Special Riemannian manifolds (Einstein, Sasakian, etc.)