We consider a unit speed curve α in Euclidean four-dimensional space E and denote the Frenet frame by {T,N,B1,B2}. We say that α is a slant helix if its principal normal vector N makes a constant angle with a fixed direction U . In this work we give different characterizations of such curves in terms of their curvatures. MSC: 53C40, 53C50

In this study, we introduce the natural mate and conjugate of a Frenet curve in three dimensional Lie group $ \mathbb{G} with bi-invariant metric. Also, give some relationships between its or $. Especially, obtain results for when is general helix, slant spherical curve, rectifying Salkowski (constant curvature non-constant torsion), anti-Salkowski (non-constant constant Bertrand curve. Finally...

In this paper, we analyse the proper curve $\gamma(s)$ lying on pseudo-sphere. We develop an orthogonal frame $\lbrace V_{1}, V_{2}, V_{3} \rbrace$ along curve, pseudosphere. Next, find condition for to become $V_{k} -$ slant helix in Minkowski space. Moreover, another $\beta(\bar{s})$ pseudosphere or hyperbolic plane heaving $V_{2} = \bar{V_{2}}$ which \bar{V_{1}},\bar{V_{2}},\bar{V_{3}} \rbra...

Object of study in the present paper are slant and Legendre null curves 3-dimensional Sasaki-like almost contact B-metric manifolds. For examined we express general Frenet frame for which original parameter is distinguished, as well corresponding curvatures, terms structure on manifold. We prove that curvatures a framed curve constants if only specific function considered manifolds constant. fi...

In this paper, we study the geodesic, asymptotic and slant helical trajectories according to PAFORS in three-dimensional Euclidean space give some characterizations on them. Also, explain how determine helix axis for (according PAFORS). Moreover, develop a method which enables us find trajectory (if exists) lying given implicit surface accepts fixed unit direction as an angle constant angle. Th...

‎we prove that there do not exist totally contact umbilical‎ ‎proper slant lightlike submanifolds of indefinite sasakian manifolds other than totally contact geodesic‎ ‎proper slant lightlike submanifolds‎. ‎we also prove that there do‎ ‎not exist totally contact umbilical proper slant lightlike‎ ‎submanifolds of indefinite sasakian space forms‎.

A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...

‎We prove that there do not exist totally contact umbilical‎ ‎proper slant lightlike submanifolds of indefinite Sasakian manifolds other than totally contact geodesic‎ ‎proper slant lightlike submanifolds‎. ‎We also prove that there do‎ ‎not exist totally contact umbilical proper slant lightlike‎ ‎submanifolds of indefinite Sasakian space forms‎.