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)
The slant helices according to bishop frame of the spacelike curve in Lorentzian space. (English) Zbl 1190.53015
T. Ikawa obtained the following differential equation $$D_TD_TD_TT-KD_TT, \quad K = \kappa^2-\tau^2$$ for the circular helix which corresponds the case when the curvature $\kappa$ and torsion $\tau$ of space-like curve with a space-like binormal $\alpha$ on the Lorentzian manifold $M_1$ are constant [{\it T. Ikawa}, Tsukuba J. Math. 9, 353--371 (1985; Zbl 0588.53017)]. In this paper, we define a slant helix with the help of the Bishop frame of the space-like curve with a space-like binormal. Furthermore, we give some necessary and sufficient conditions for the slant helix and T. Ikawa’s result is generalized to the case of the general slant helix.

53B25Local submanifolds
53B30Lorentz metrics, indefinite metrics
Full Text: DOI