In this book, the global differential geometry of Weingarten surfaces and hypersurfaces in E4 had been discussed. 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 additional conditions had been discussed.
In this book, the global differential geometry of Weingarten surfaces and hypersurfaces in E4 had been discussed. This leads to apply some global meth...
The conic sections are represented in non real §planes using a new real plane called the Entire §plane. We proved by using two methods (Cartan §structure equations and Christoffel Symbol of the §Second Kind) that the non real planes and with §suitable metrics are hyperbolic planes and the §geodesics in these planes are hyperbolic straight §lines. The seven non real spaces of three §dimensions and are distinguished. A proof is §introduced showing that these non real spaces with §suitable metrics are hyperbolic spaces. The surfaces §of second degree are represented in these non real...
The conic sections are represented in non real §planes using a new real plane called the Entire §plane. We proved by using two methods (Cartan §str...
