Dupin hypersurfaces
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Publication:793340
DOI10.1007/BF01473438zbMath0538.53004OpenAlexW4253725390MaRDI QIDQ793340
Publication date: 1985
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/182970
Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)
Related Items (45)
Plane curves in Lie sphere geometry ⋮ Buckling eigenvalues, Gauss maps and Lagrangian submanifolds ⋮ Dupin hypersurfaces and integrable Hamiltonian systems of hydrodynamic type which do not possess Riemann invariants ⋮ Tautness and Lie sphere geometry ⋮ ANALOG OF WILCZYNSKI'S PROJECTIVE FRAME IN LIE SPHERE GEOMETRY: LIE-APPLICABLE SURFACES AND COMMUTING SCHRÖDINGER OPERATORS WITH MAGNETIC FIELDS ⋮ Isothermal hypersurfaces and three-dimensional Dupin-Mannheim hypercyclides ⋮ Deformation and applicability of surfaces in Lie sphere geometry ⋮ Spacelike Dupin hypersurfaces in Lorentzian space forms ⋮ Laguerre homogeneous surfaces in \(\mathbb R^3\) ⋮ On Dupin hypersurfaces in \(\mathbb R^{5}\) parametrized by lines of curvature ⋮ Laguerre geometry of hypersurfaces in \({\mathbb R}^n\) ⋮ The second variational formula for Laguerre minimal hypersurfaces in \(\mathbb R^n\) ⋮ Deformations of Dupin Hypersurfaces ⋮ Möbius curvature, Laguerre curvature and Dupin hypersurface ⋮ Computation of Yvon-Villarceau circles on Dupin cyclides and construction of circular edge right triangles on tori and Dupin cyclides ⋮ Isoparametric hypersurfaces in spheres, integrable nondiagonalizable systems of hydrodynamic type, and \(N\)-wave systems ⋮ Dupin hypersurfaces with constant Laguerre curvatures ⋮ Homogeneous surfaces in Lie sphere geometry ⋮ Classification of hypersurfaces with two distinct principal curvatures and closed Möbius form in \(\mathbb{S}^{m + 1}\) ⋮ Classifications of Dupin hypersurfaces in Lie sphere geometry ⋮ Möbius geometry for hypersurfaces in S4 ⋮ Curvature line parametrized surfaces and orthogonal coordinate systems: discretization with Dupin cyclides ⋮ Laguerre isoparametric hypersurfaces in \(\mathbb R^n\) with two distinct non-zero principal curvatures ⋮ Dupin hypersurfaces with four principal curvatures in \(\mathbb R^{5}\) with principal coordinates ⋮ On the Lie curvature of Dupin hypersurfaces ⋮ Polynomial conserved quantities of Lie applicable surfaces ⋮ Finiteness results for equifocal hypersurfaces in compact symmetric spaces ⋮ Dupin hypersurfaces with four principal curvatures. II. ⋮ Channel surfaces in Lie sphere geometry ⋮ On congruences of Laguerre cycles and their envelopes ⋮ On a class of Dupin hypersurfaces in \(\mathbb R^5\) with nonconstant Lie curvature ⋮ Laguerre minimal surfaces in \(\mathbb R^{3}\) ⋮ Submanifolds with flat normal bundle ⋮ An extrinsic decomposition theorem and a slant tube theorem for a curvature netted hypersurface ⋮ On a class of submanifolds carrying an extrinsic totally umbilical foliation. ⋮ The quadratic slice theorem and the equiaffine tube theorem for equiaffine Dupin hypersurfaces ⋮ Lie sphere geometry in Hilbert spaces ⋮ On four dimensional Dupin hypersurfaces in Euclidean space ⋮ Dupin hypersurfaces and a Lie invariant ⋮ Taut representations of compact simple Lie groups ⋮ A characterization of Moebius isoparametric hypersurfaces of the sphere ⋮ Lie Sphere Transformations and the Focal Sets of Certain Taut Immersions ⋮ Highly connected taut submanifolds ⋮ Lie sphere geometry and integrable systems. ⋮ Lie contact structures and normal Cartan connections
Cites Work
- Domaines symétriques des quadriques projectives
- Curvature properties of taut submanifolds
- Symmetric submanifolds of Euclidean space
- Focal sets of submanifolds
- Homogeneity and some curvature conditions for hypersurfaces
- Dupin Hypersurfaces
- Conformal Geometry and the Cyclides of Dupin
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