Titlebook: Surfaces in Classical Geometries; A Treatment by Movin Gary R. Jensen,Emilio Musso,Lorenzo Nicolodi Textbook 2016 Springer International Pu

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,Möbius Geometry,jection these are all globally defined conformal transformations of the sphere ... The Möbius group . is the group of all conformal transformations of ... It is a ten dimensional Lie group containing the group of isometries of each of the space forms as a subgroup. Möbius space . is the homogeneous

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,Isothermic Immersions into Möbius Space,face in Möbius space. Thus, an isothermic immersion in a space form remains isothermic under conformal transformations. An isothermic immersion into Möbius space is special if it comes from a CMC immersion into a space form. By a theorem of Voss, the Bryant quartic differential form of an umbilic fr

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Minimal Immersions in Euclidean Space,ons in Euclidean space that smoothly extend to compact Will more immersions into Möbius space. The final section on minimal curves applies the method of moving frames to the nonintuitive setting of holomorphic curves in .. whose tangent vector is nonzero and isotropic at every point.

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Theory of Moving Frames,e after first describing the procedure for the elementary example of curves in the punctured plane acted upon by the special linear group .(2, .). The chapter concludes with basic theorems that characterize when a submanifold of a homogeneous space is itself homogeneous.

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Hyperbolic Geometry,s of tangent and curvature spheres of an immersed surface are described in detail as preparation for their fundamental role in Lie sphere geometry. The chapter concludes with many elementary examples.

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Textbook 2016to relevant topics in classical differential geometry. The method of moving frames, a natural means for discovering and proving important results, provides the basis of treatment for topics discussed. Its application in many areas helps to connect the various geometries and to uncover many deep rela