On general helices and pseudo-riemannian manifolds

Authors : N. EKMEKÇİ

Pages : 0-0

Doi:10.1501/Commua1_0000000404

View : 8 | Download : 6

Publication Date : 1998-01-01

Article Type : Research Paper

Abstract :In a Riemannian manifold, a regular curve is called a general helix if is constant and its firs and second curvatures are not constant [4]. İf its First and second curvatures are constant the third curvature is zero then the regular curve is called helix. For helices in a Lorentzian manifold, there is a research of T. Ikawa, who investigated and obtained the differential equation; D D D X = KD X , insert ignore into journalissuearticles values(K = a - p5 XXX X fOT the drcular helix which corresponds to the case that the curvatures a and P of the timelike curve cinsert ignore into journalissuearticles values(t); on the Lorentzian manifold M are constant [3], Later, N. Ekmekçi and H.H. HacısaUhoğlu obtained the differential equation I\I\DxX = KD^K + 3a` D^Y , K = of + a2 P`); P fcff the case of general helix [2]. Recently, T. Nakanishi [5] prove the following lemma about a helix in Pseudo-Riemannian manifold which is stated as, “A unit speed curve c in M is a helix if and only if there exist a constant X such that D D D X = XD X” XXX X a îhis paper generalizes the lemma stated above lo the case of a general helix.
Keywords : general helices, pseudo riemannian, manifolds