Titlebook: Geometry of Hypersurfaces; Thomas E. Cecil,Patrick J. Ryan Book 2015 Thomas E. Cecil and Patrick J. Ryan 2015 Dupin hypersurfaces.Hopf hyp

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Submanifolds in Lie Sphere Geometry,upin hypersurfaces this has proven to be a valuable approach, since Dupin hypersurfaces occur naturally as envelopes of families of spheres, which can be handled well in Lie sphere geometry. Since the Dupin property is invariant under Lie sphere transformations, this is also a natural setting for cl

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Dupin Hypersurfaces,sphere geometry, and many classification results have been obtained in that setting. In this chapter, we will use the viewpoint of the metric geometry of . as well as that of Lie sphere geometry to obtain results about Dupin hypersurfaces.

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Real Hypersurfaces in Complex Space Forms,on isoparametric hypersurfaces in spheres. A key early work was Takagi’s classification [669] in 1973 of homogeneous real hypersurfaces in ... These hypersurfaces necessarily have constant principal curvatures, and they serve as model spaces for many subsequent classification theorems. Later Montiel

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Hopf Hypersurfaces,Berndt [30] in .. (see Theorem?8.12). These classifications state that such a hypersurface is an open subset of a hypersurface on Takagi’s list for .., and on Montiel’s list for ... We then study several characterizations of these hypersurfaces based on conditions on their shape operators, curvature

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978-1-4939-4507-8Thomas E. Cecil and Patrick J. Ryan 2015

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https://doi.org/10.1007/978-1-4939-3246-7Dupin hypersurfaces; Hopf hypersurfaces; Lie sphere geometry; differential geometry submanifolds; geomet

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