Dupin hypersurface

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In differential geometry, a Dupin hypersurface is a submanifold in a space form, whose principal curvatures have globally constant multiplicities.[1]


A hypersurface is called a Dupin hypersurface if the multiplicity of each principal curvature is constant on hypersurface and each principal curvature is constant along its associated principal directions.[2] All proper Dupin submanifolds arise as focal submanifolds of proper Dupin hypersurfaces.[3]


  1. ^ K. Shiohama (4 October 1989). Geometry of Manifolds. Elsevier. pp. 181–. ISBN 978-0-08-092578-3. 
  2. ^ Themistocles M. Rassias (1992). The Problem of Plateau: A Tribute to Jesse Douglas & Tibor Radó. World Scientific. pp. 61–. ISBN 978-981-02-0556-0. 
  3. ^ Robert Everist Greene; Shing-Tung Yau (1993). Partial Differential Equations on Manifolds. American Mathematical Soc. pp. 466–. ISBN 978-0-8218-1494-9. 
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