We define the fundamental region homeomorphic to the corresponding Riemann surface according to the methods on form-conserved circle of the fractional linear transformation in explaining that the form-conserved circle...We define the fundamental region homeomorphic to the corresponding Riemann surface according to the methods on form-conserved circle of the fractional linear transformation in explaining that the form-conserved circle is the perpendicular bisector of noneuclidean segment limited by the end points both the origin and the equivalent point by the same transformation just mentioned and, consequently, its sense on noneuclidean geometry is clarified.The result does not appear in current literatures and is useful for the research of superstring.展开更多
Let D={z∈C: │z│【1} be the unit disk in the finite complex plane C and Г a Fuchsiangroup consisting of Mbius maps from D to itself. Also, let Ω={z∈D:│z│【│γz│, id≠γ∈Г}be the fundamental region unde Г. ...Let D={z∈C: │z│【1} be the unit disk in the finite complex plane C and Г a Fuchsiangroup consisting of Mbius maps from D to itself. Also, let Ω={z∈D:│z│【│γz│, id≠γ∈Г}be the fundamental region unde Г. Put Ω=D when Г={id}. If we denote by Ω andΩ the closure and boundary of Ω on D, respectively, then we know that Ω has展开更多
文摘We define the fundamental region homeomorphic to the corresponding Riemann surface according to the methods on form-conserved circle of the fractional linear transformation in explaining that the form-conserved circle is the perpendicular bisector of noneuclidean segment limited by the end points both the origin and the equivalent point by the same transformation just mentioned and, consequently, its sense on noneuclidean geometry is clarified.The result does not appear in current literatures and is useful for the research of superstring.
文摘Let D={z∈C: │z│【1} be the unit disk in the finite complex plane C and Г a Fuchsiangroup consisting of Mbius maps from D to itself. Also, let Ω={z∈D:│z│【│γz│, id≠γ∈Г}be the fundamental region unde Г. Put Ω=D when Г={id}. If we denote by Ω andΩ the closure and boundary of Ω on D, respectively, then we know that Ω has
