Geometry of Hypersurfaces - Ryan Patrick J.
Geometry of Hypersurfaces - Ryan Patrick J. This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. The book is…
Specifikacia Geometry of Hypersurfaces - Ryan Patrick J.
Geometry of Hypersurfaces - Ryan Patrick J.
This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms.
Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area.Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. The focus then turns to the theory of isoparametric hypersurfaces in spheres.
Important examples and classification results are
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