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2004•Communications Faculty Of Science University of Ankara Series A1Mathematics and StatisticsOpen access

Osculating spheres and osculating circles of a curve in semi-riemannian space

Derya Sağlam, Kazım İlarslan, Emine Soytürk

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Abstract

Ilı the Euclidean 3-space, t,here is a uııigue sphere for a curve o : / —» R^ such that the sphere touchc.s a at. the third order at ct(0). The iııtersectioıı of the splıere with oseulatiııg plaııe is a eircle which touches a at the secoud order at a(0) [5j. In this paper, the osculating sphere and the osculating circle of the curve are studied for each of timelike, spacelike and null (Ughtlike) curves in Semi-Riemannian Spaces; Rj, R| and R^.

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Ilı the Euclidean 3-space, t,here is a uııigue sphere for a curve o : / —» R^ such that the sphere touchc.s a at. the third order at ct(0). The iııtersectioıı of the splıere with oseulatiııg plaııe is a eircle which touches a at the secoud order at a(0) [5j. In this paper, the osculating sphere and the osculating circle of the curve are studied for each of timelike, spacelike and null (Ughtlike) curves in Semi-Riemannian Spaces; Rj, R| and R^.

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Available abstract

Ilı the Euclidean 3-space, t,here is a uııigue sphere for a curve o : / —» R^ such that the sphere touchc.s a at. the third order at ct(0). The iııtersectioıı of the splıere with oseulatiııg plaııe is a eircle which touches a at the secoud order at a(0) [5j. In this paper, the osculating sphere and the osculating circle of the curve are studied for each of timelike, spacelike and null (Ughtlike) curves in Semi-Riemannian Spaces; Rj, R| and R^.

Key concepts: Osculating circle, Mathematics, SPHERES, Euclidean geometry, Space (punctuation), Mathematical analysis, Euclidean space, Order (exchange)

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