Dupin hypersurface

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.
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.
Robert Everist Greene; Shing-Tung Yau (1993). Partial Differential Equations on Manifolds. American Mathematical Soc. pp. 466–. ISBN 978-0-8218-1494-9.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

[Shiohama1989-1] K. Shiohama (4 October 1989). Geometry of Manifolds. Elsevier. pp. 181–. ISBN 978-0-08-092578-3.

[Rassias1992-2] 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.

[GreeneYau1993-3] Robert Everist Greene; Shing-Tung Yau (1993). Partial Differential Equations on Manifolds. American Mathematical Soc. pp. 466–. ISBN 978-0-8218-1494-9.