Interpolation of Markoff transformations on the Fricke surface
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概要
- 論文の詳細を見る
By the Fricke surfaces, we mean the cubic surfaces defined by the equation $p^2+q^2+r^2-pqr-k=0$ in the Euclidean 3-space with the coordinates $(p,q,r)$ parametrized by constant $k$. When $k=0$, it is naturally isomorphic to the moduli of once-punctured tori. It was Markoff who found the transformations, called Markoff transformations, acting on the Fricke surface. The transformation is typically given by $(p,q,r)\mapsto (r,q,rq-p)$ acting on $\boldsymbol{R}^3$ that keeps the surface invariant. In this paper we propose a way of interpolating the action of Markoff transformation. As a result, we show that one portion of the Fricke surface with $k=4$ admits a ${\rm GL}(2,\boldsymbol{R})$-action extending the Markoff transformations.
著者
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Sasaki Takeshi
Department of Rheumatology, Tohoku University school of Medicine
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YOSHIDA Masaaki
Department of Electrical and Computer Engineering, Hachinohe National College of Technology
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Yoshida Masaaki
Department Of Electrical And Computer Engineering Hachinohe National College Of Technology
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Sasaki Takeshi
Department Of Mathematics Kobe University
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Sasaki Takeshi
Department Of Agricultural Chemistry Faculty Of Agriculture Ehime University
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Yoshida Masaaki
Department Of Mathematics Kyushu University
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Yoshida Masaaki
Department Of Biology Graduate School Of Science Osaka University
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Yoshida Masaaki
Department Of Applied Chemistry Faculty Of Engineering Utsunomiya University
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Sasaki Takeshi
Department of Mathematics, Kobe University
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