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Elastica and inextensible flows of curves play an important role in practical applications. In this paper, we construct a new characterization of inextensible flows by using elastica in space. The inextensible flow is completely determined for any space-like curve in de Sitter space [...] S 1 3 ${𝕊}_1^3$. Finally, we give some characterizations for curvatures of a space-like curve in de Sitter space [...] S 1 3 ${𝕊}_1^3$.