Hüseyin Kocayiğit

DIFFERENTIAL EQUATIONS CHARACTERIZING TIMELIKE AND SPACELIKE CURVES OF CONSTANT BREADTH IN MINKOWSKI 3-SPACE E 1 3

In this paper, we give the differential equations characterizing the timelike and spacelike curves of constant breadth in Minkowski 3-space . Furthermore, we give a criterion for a timelike or spacelike curve to be the curve of constant breadth in . As an example, the obtained results are applied to the case = const. and = const., and are discussed.

Some characterizations of the slant helices according to N-Bishop frame in Euclidean 3-space

A slant helix is a kind of helix whose normal line makes a const a t angle with a fixed direction. Due to the diversity of the application areas of the slant helices, a lot of work has b een done in recent years. In this paper, some characterizati ons of the slant helices according to N-Bishop Frame in Euclidean 3space ar e given.

CHARACTERIZATIONS OF SPACE CURVES WITH 1-TYPE DARBOUX INSTANTANEOUS ROTATION VECTOR

Abstract. In this study, by using Laplace and normal Laplace operators,we give some characterizations for the Darboux instantaneous rotationvector field of the curves in the Euclidean 3-space E 3 . Further, we givenecessary and sufficient conditions for unit speed space curves to have1-type Darboux vectors. Moreover, we obtain some characterizations ofhelices according to Darboux vector. 1. IntroductionOne of the most important problems of local differential geometry is toobtain the relations characterizingspecial curves with respect to their curvatureand torsion. The well-known types of such special curves are constant slopecurves or general helices which are defined by the property that the tangentvectors of curves make a constant angle with fixed directions. A necessaryand sufficient condition for a curve to be a general helix in the Euclidean 3-space E 3 is that the ratio of curvature to torsion is constant [11]. So, manymathematicians have focused their studies on these special curves in differentspaces such as Euclidean space and Minkowski space [3, 4, 5, 10].Furthermore, Chen and Ishikawa [1] classified biharmonic curves, the curvesfor which ∆H~ = 0 holds in semi-Euclidean space E

Characterizations of timelike curves according to the Bishop Darboux vector in Minkowski 3-space E_1^3

In this paper, we obtained some characterizations o f timelike curves according to Bihop frame in Minkowski 3-space 3 1 E by using Laplacian operator and Levi-Civita connection. Furthermore we gave the g neral differential equations which characterize the timelike curves ac cording to the Bishop Darboux vector and the normal Bishop Darboux vector. Mathematics Subject Classification : 53A04, 53B30, 53A35.