Lie Sphere Transformations and the Focal Sets of Certain Taut Immersions

DOI10.2307/2001019zbMath0658.53056OpenAlexW4235380432WikidataQ57316087 ScholiaQ57316087MaRDI QIDQ3806325

Steven G. Buyske

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2001019

zbMATH Keywords

tightnessDupin hypersurfaceLie sphere geometrytautness

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Lie geometries in nonlinear incidence geometry (51B25)

Cites Work

• Isoparametrische Hyperflächen in Sphären. I
• Compact Dupin hypersurfaces with three principal curvatures
• Dupin hypersurfaces
• Curvature properties of taut submanifolds
• On critical sets of distance function to a taut submanifold
• Tautness and Lie sphere geometry
• Focal sets, taut embeddings and the cyclides of Dupin
• Isoparametric submanifolds and their Coxeter groups
• Homogeneity and some curvature conditions for hypersurfaces
• Dupin Hypersurfaces
• Deformations of Dupin Hypersurfaces
• A global formulation of the Lie theory of transformation groups
• Tight and Taut Immersions
• Umbilical Submanifolds and Morse Functions
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