Classical Differential Geometry of Curves According to Type-2 Bishop Trihedra

ASSOCIATED CURVES OF THE SPACELIKE CURVE VIA THE BISHOP FRAME OF TYPE-2 IN E₁³

The objective of the study in this paper is to define M₁,M₂-direction curves and M₁,M₂-donor curves of the spacelike curve γ via the Bishop frame of type-2 in E₁³. We obtained the necessary and sufficient conditions when the associated curves to be slant helices and general helices via the Bishop frame of type-2 in E₁³. After defining the spherical indicatrices of the associated curves, we obta...

DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES 2. Curves in Space

for a < t < b. The entire Section 1.3 of the notes can be immediately reformulated for curves in the space: Definition 1.3.2 (of the length of a curve over a closed interval), Definition 1.3.3 and Theorem 1.3.4 (concerning reparametrization of curves), Definition 1.3.4 (of a regular curve), Theorem 1.3.6 and Proposition 1.3.7 (concerning parametrization by arc length). As about Section 1.4 (tha...

Contributions to differential geometry of spacelike curves in Lorentzian plane L2

‎In this work‎, ‎first the differential equation characterizing position vector‎ ‎of spacelike curve is obtained in Lorentzian plane $mathbb{L}^{2}.$ Then the‎ ‎special curves mentioned above are studied in Lorentzian plane $mathbb{L}%‎‎^{2}.$ Finally some characterizations of these special curves are given in‎ ‎$mathbb{L}^{2}.$‎

Classical Differential Geometry

contributions to differential geometry of spacelike curves in lorentzian plane l2

‎in this work‎, ‎first the differential equation characterizing position vector‎ ‎of spacelike curve is obtained in lorentzian plane $mathbb{l}^{2}.$ then the‎ ‎special curves mentioned above are studied in lorentzian plane $mathbb{l}%‎‎^{2}.$ finally some characterizations of these special curves are given in‎ ‎$mathbb{l}^{2}.$‎