INTEGRAL CHARACTERIZATIONS FOR TIMELIKE AND SPACELIKE CURVES ON THE LORENTZIAN SPHERE S31

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KAZAZ M.; UGURLU H.H.; OZDEMIR A.

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Journal: IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE Year:2008 | Volume:32 | Issue:A1 Page(s): 25-31

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Title

INTEGRAL CHARACTERIZATIONS FOR TIMELIKE AND SPACELIKE CURVES ON THE LORENTZIAN SPHERE S31

Author(s)

KAZAZ M. | UGURLU H.H. | OZDEMIR A. | Issue Writer Certificate

Keywords

LORENTZIAN 3-SPHERE

TIMELIKE CURVE

SPACELIKE CURVE

CURVATURE

Abstract

V. Dannon showed that spherical curves in E4 can be given by Frenet-like equations, and he then gave an integral characterization for spherical curves in E4 . In this paper, Lorentzian spherical timelike and SPACELIKE CURVEs in the space time R41 are shown to be given by Frenet-like equations of timelike and SPACELIKE CURVEs in the Euclidean space E3 and the Minkowski 3-space R31. Thus, finding an integral characterization for a Lorentzian spherical R41 -timelike and SPACELIKE CURVE is identical to finding it for E3 curves and R31 -timelike and SPACELIKE CURVEs. In the case of E3 curves, the integral characterization coincides with Dannon’s. Let {T, N, B} be the moving Frenet frame along the curve a(s) in the Minkowski space R31. Let a(s) be a unit speed C4 -timelike (or spacelike) curve in R31 so that a'(s)=T. Then, a(s) is a Frenet curve with CURVATURE k s) and torsion t(s) if and only if there are constant vectors a and b so that (i)T’(s)= k(s){a cos x(s)+b sin x(s)+ òs0 cos[x(s)- x(d)] T(d)k(d)dd}, T is timelike, (ii) T’(s)= k{aex+bex òs0 cosh (x(s)- x(s)- T(d)k(d)dd}, n is timelike, where x(s)+ òs0t(d)dd.

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APA: Copy

KAZAZ, M., UGURLU, H.H., & OZDEMIR, A.. (2008). INTEGRAL CHARACTERIZATIONS FOR TIMELIKE AND SPACELIKE CURVES ON THE LORENTZIAN SPHERE S³_{1. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE, 32(A1), 25-31. SID. https://sid.ir/paper/548367/en}

Vancouver: Copy

KAZAZ M., UGURLU H.H., OZDEMIR A.. INTEGRAL CHARACTERIZATIONS FOR TIMELIKE AND SPACELIKE CURVES ON THE LORENTZIAN SPHERE S³_{1. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE[Internet]. 2008;32(A1):25-31. Available from: https://sid.ir/paper/548367/en}

IEEE: Copy

M. KAZAZ, H.H. UGURLU, and A. OZDEMIR, “INTEGRAL CHARACTERIZATIONS FOR TIMELIKE AND SPACELIKE CURVES ON THE LORENTZIAN SPHERE S³_{1,” IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE, vol. 32, no. A1, pp. 25–31, 2008, [Online]. Available: https://sid.ir/paper/548367/en}

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