By Thomas E. Cecil,Patrick J. Ryan
This exposition presents the state-of-the paintings at the differential geometry of hypersurfaces in actual, advanced, and quaternionic area varieties. designated emphasis is put on isoparametric and Dupin hypersurfaces in actual area kinds in addition to Hopf hypersurfaces in advanced area types. The ebook is obtainable to a reader who has accomplished a one-year graduate path in differential geometry. The textual content, together with open difficulties and an in depth record of references, is a superb source for researchers during this area.
Geometry of Hypersurfaces starts with the fundamental thought of submanifolds in actual area kinds. issues contain form operators, critical curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. the point of interest then turns to the idea of isoparametric hypersurfaces in spheres. very important examples and class effects are given, together with the development of isoparametric hypersurfaces according to representations of Clifford algebras. An in-depth therapy of Dupin hypersurfaces follows with effects which are proved within the context of Lie sphere geometry in addition to those who are received utilizing average equipment of submanifold conception. subsequent comes an intensive remedy of the idea of genuine hypersurfaces in complicated house forms. A principal concentration is a whole evidence of the type of Hopf hypersurfaces with consistent significant curvatures because of Kimura and Berndt. The booklet concludes with the elemental thought of genuine hypersurf
aces in quaternionic house varieties, together with statements of the key class effects and instructions for extra research.
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Geometry of Hypersurfaces (Springer Monographs in Mathematics) by Thomas E. Cecil,Patrick J. Ryan
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