E-grāmata: Global Affine Differential Geometry of Hypersurfaces 2nd [De Gruyter E-books]

Japanese geometers introduce global affine hypersurface theory to students who have a basic knowledge of Euclidean differential geometry (curves and hypersurfaces) and Riemannian geometry. This second edition incorporates developments in the field during the 20 years since the first. It covers preliminaries and basic structural aspects, local equiaffine hypersurface theory, affine hyperspheres, rigidity and uniqueness theorems, variational problems and affine maximal surfaces, hypersurfaces with constant affine Gauss-Kronecker curvature, and geometric inequalities. Appendices review basic concepts in differential geometry and Laplacian comparison theorem. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)

This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry- as differential geometry in general- has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.