This exposition presents the state-of-the artwork at the differential geometry of hypersurfaces in actual, complicated, and quaternionic area types. targeted emphasis is put on isoparametric and Dupin hypersurfaces in genuine house types in addition to Hopf hypersurfaces in advanced area types. The e-book is on the market to a reader who has accomplished a one-year graduate direction in differential geometry. The textual content, together with open difficulties and an intensive checklist of references, is a superb source for researchers during this area.
Geometry of Hypersurfaces starts off with the elemental concept of submanifolds in genuine area varieties. issues comprise form operators, valuable 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 type effects are given, together with the development of isoparametric hypersurfaces in keeping with 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 acquired utilizing general tools of submanifold concept. subsequent comes a radical remedy of the idea of genuine hypersurfaces in advanced area forms. A valuable concentration is an entire facts of the category of Hopf hypersurfaces with consistent imperative curvatures as a result of Kimura and Berndt. The e-book concludes with the elemental idea of genuine hypersurfaces in quaternionic area types, together with statements of the most important class effects and instructions for extra research.
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