Evolutes of Hyperbolic Dual Spherical Curve in Dual Lorentzian 3-Space

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Based on the E. Study's map, we study a timelike ruled surface as a curve on the hyperbolic dual unit sphere in dual Lorentzian 3-space $\mathbb{D}_{1}^{3}$. Then, as applications of the singularity theory of smooth functions, we define the notation of evolutes for timelike ruled surfaces and establish the relationships between their geometric invariants. Finally, an example of application is introduced and explained in detail.

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