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]
Application
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]
References
- ↑ K. Shiohama (4 October 1989). Geometry of Manifolds. Elsevier. pp. 181–. ISBN 978-0-08-092578-3. https://books.google.com/books?id=yXvNCgAAQBAJ&pg=PA181.
- ↑ 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. https://books.google.com/books?id=j-O7vMJIIpgC&pg=PA61.
- ↑ Robert Everist Greene; Shing-Tung Yau (1993). Partial Differential Equations on Manifolds. American Mathematical Soc.. pp. 466–. ISBN 978-0-8218-1494-9. https://books.google.com/books?id=ulgECAAAQBAJ&dq=Dupin+hypersurface&pg=PA466.
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