|
In hyperbolic geometry, an earthquake map is a method of changing one hyperbolic manifold into another, introduced by . ==Earthquake maps== Given a simple geodesic on an oriented hyperbolic manifold and a real number ''t'', one can cut the manifold along the geodesic, slide the edges a distance ''t'' to the left, and glue them back. This gives a new hyperbolic manifold, and the (possibly discontinuous) map between them is an example of a left earthquake. More generally one can do the same construction with a finite number of disjoint simple geodesics, each with a real number attached to it. The result is called a simple earthquake. An earthquake is roughly a sort of limit of simple earthquakes, where one has an infinite number of geodesics, and instead of attaching a positive real number to each geodesic one puts a measure on them. A geodesic lamination of a hyperbolic surface is a closed subset with a foliation by geodesics. A left earthquake ''E'' consists of a map between copies of the hyperbolic plane with geodesic laminations, that is an isometry from each stratum of the foliation to a stratum. Moreover if ''A'' and ''B'' are two strata then ''E'E'' is a hyperbolic transformation whose axis separates ''A'' and ''B'' and which translates to the left, where ''E''''A'' is the isometry of the whole plane that restricts to ''E'' on ''A'', and likewise for ''B''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「earthquake map」の詳細全文を読む スポンサード リンク
|