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2010•Journal of Dynamical Systems and Geometric TheoriesRequires access

Time-Like Smarandache Curves Derived from a Space-Like Helix

Ahmad T. Ali

Open publisher page 4 citations

Abstract

A regular curve in Minkowski space-time , whose position vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache curve. We define a special case of such curves and call it Smarandache TB2 curves in the Minkowski space-time . Moreover, we compute formulas of its Frenet apparatus according to base curve via the method expressed in [5, 6]. By this way, we obtain another orthonormal frame of a such curve in .

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What this paper is about

A regular curve in Minkowski space-time , whose position vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache curve. We define a special case of such curves and call it Smarandache TB2 curves in the Minkowski space-time . Moreover, we compute formulas of its Frenet apparatus according to base curve via the method expressed in [5, 6]. By this way, we obtain another orthonormal frame of a such curve in .

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Available abstract

A regular curve in Minkowski space-time , whose position vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache curve. We define a special case of such curves and call it Smarandache TB2 curves in the Minkowski space-time . Moreover, we compute formulas of its Frenet apparatus according to base curve via the method expressed in [5, 6]. By this way, we obtain another orthonormal frame of a such curve in .

Key concepts: Frenet–Serret formulas, Minkowski space, Mathematics, Base (topology), Mathematical analysis, Space (punctuation), Ruled surface, Frame (networking)

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