In this book the global differential geometry ofWeingarten surfaces and hypersurfaces in E4 had beendiscussed. This leads to apply some global methods on a class of Weingarten surfaces and hyper surfaces satisfying umbilical boundary conditions. Also the characterization of hyperspheres among the umbilical boundary conditions (U.B.C.) Weingarten hypersurfaces with some additionalconditions had been discussed.
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