A Method of the Determination of a Geodesic Curve on Ruled Surface with Time-like Rulings
نویسندگان
چکیده
A non-linear differential equation is analyzed to determine the geodesic curves on ruled surfaces with time-like rulings inR31. When it is assumed that curvature and torsion of the base curve and components with respect to Frenet’s frame of time-like straight-line are constants, for a special integration constant, it appears that the resulting non-linear differential equation can be integrated exactly. Finally, examples are given to show the geodesic curve on ruled surfaces with time-like rulings. AMS Mathematics Subject Classification (2000): 58E10
منابع مشابه
A Method of the Determination of a Geodesic Curve on Timelike Ruled Surface with Spacelike Rulings
A curve which is called geodesic on a surface M in Lorentz 3-space is a special curve that its acceleration is everywhere normal to M. In this paper, we analyzed the non-linear differential equation to determine the geodesic curves on ruled surfaces which is obtained by a strictly connected spacelike straight line moving with Frenet’s frame along a timelike curve in . When we assume that curvat...
متن کاملErratum to: "Ruled surfaces with time like rulings" [Appl. Math. Comput. 147(2004) 241-248]
In this article, a new type of ruled surfaces in a Lorentz 3-space R31 is obtained by a strictly connected time-like oriented line moving with Frenet s frame along a space-like curve. These surfaces are classified into time-like and space-like surfaces. The wellknown theorems due to Bonnet and Chasles in the 3-dimensional Euclidean space are proved for a time-like ruled surface. 2005 Published ...
متن کاملConstruction of a surface pencil with a common special surface curve
In this study, we introduce a new type of surface curves called $D$-type curve. This curve is defined by the property that the unit Darboux vector $vec{W}_{0} $ of a surface curve $vec{r}(s)$ and unit surface normal $vec{n} $ along the curve $vec{r}(s)$ satisfy the condition $leftlangle vec{n} ,vec{W}_{0} rightrangle =text{constant}$. We point out that a $D$-type curve is a geodesic curve or an...
متن کاملENTROPY OF GEODESIC FLOWS ON SUBSPACES OF HECKE SURFACE WITH ARITHMETIC CODE
There are dierent ways to code the geodesic flows on surfaces with negative curvature. Such code spaces give a useful tool to verify the dynamical properties of geodesic flows. Here we consider special subspaces of geodesic flows on Hecke surface whose arithmetic codings varies on a set with innite alphabet. Then we will compare the topological complexity of them by computing their topological ...
متن کاملErratum to: "Ruled surfaces with timelike rulings" [Appl. Math. Comput. 147: (2004) 241-253]
In this paper, using [E. Kasap, _ I. Aydemir, N. Kuruoğlu, Erratum to: ‘‘Ruled surfaces with timelike rulings’’ [Appl. Math. Comput. 147 (2004) 241–253], Applied Mathematics and Computation 168 (2005) 1461–1468 [2]], some mistakes which are related to the classification maximal ruled surfaces with timelike rulings in the last section of [Applied Mathematics and Computation 147 (2004) 241–253 [1...
متن کامل