چكيده لاتين :
V. Dannon showed that spherical curves in E 4 can be given by Frenet-like equations, and he then
gave an integral characterization for spherical curves in E 4
. In this paper, Lorentzian spherical timelike and
spacelike curves in the space time Rt are .shown to be given by Frenet-like equations of timelike and
spacelike curves in the Euclidean space E;) and the Minkowski 3-space Rt. Thus, finding an integral
characterization for a Lorentzian spherical Rt -timelike and spacelike curve is identical to finding it for E3
curves and R}3 -timelike and spacelike curves. In the case of E 3 curves, the integral characterization
coincides with Dannonיs.
Let {T, N, B}be the moving Frenet frame along the curve a(s) in the Minkowski space R}3. Let
a(s) be a unit speed C4 -timelike (or spacelike) curve in R}3 so that a י(s) == T . Then, a(s) is a Frenet
curve with curvature K(s) and torsion r( s) if and only if there are constant vectors a and b so that
(i) Tי(s) = K(S){a eo~ S:(s)~ bsi~ S:(s)+ Lיcos [S:(s) - S:(J)] T(J)K(J) dol T is timelike,
(ii) Tי(s) = K(S}{ aei-vbe" +Leosh(S:(s)-S:(J) )T(J)K(J)dJ }, N is timelike,
where S:(s)= LT(J)dJ.
