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In this paper, as a generalization of Kiem and Castravet's works, we study the stable maps in $\\mathcal{N}$ with genus $0$ and degree $3$. Let $P$ be a natural closed subvariety of $\\mathcal{N}$ which parametrizes stable vector bundles with a fixed subbundle $L^{-1}(-x)$ for a line bundle $L$ on $X$. We describe the stable map space $\\mathbf{M}_0(P,3)$. 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Let $\\mathcal{N}$ be the moduli space of stable rank two vector bundles on $X$ with a fixed determinant $\\mathcal{O}_X(-x)$ for $x\\in X$. In this paper, as a generalization of Kiem and Castravet's works, we study the stable maps in $\\mathcal{N}$ with genus $0$ and degree $3$. Let $P$ be a natural closed subvariety of $\\mathcal{N}$ which parametrizes stable vector bundles with a fixed subbundle $L^{-1}(-x)$ for a line bundle $L$ on $X$. We describe the stable map space $\\mathbf{M}_0(P,3)$. 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