Writing this book, I had in my mind areader trying to get some knowledge of a part of the modern differential geometry. I concentrate myself on the study of sur- faces in the Euclidean 3-space, this being the most natural object for investigation. The global differential geometry of surfaces in E3 is based on two classical results: (i) the ovaloids (i.e., closed surfaces with positive Gauss curvature) with constant Gauss or mean curvature are the spheres, (u) two isometrie ovaloids are congruent. The results presented here show vast generalizations of these facts. Up to now, there is only one...

Writing this book, I had in my mind areader trying to get some knowledge of a part of the modern differential geometry. I concentrate myself on the study of sur faces in the Euclidean 3-space, this being the most natural object for investigation. The global differential geometry of surfaces in E3 is based on two classical results: (i) the ovaloids (i.e., closed surfaces with positive Gauss curvature) with constant Gauss or mean curvature are the spheres, (u) two isometrie ovaloids are congruent. The results presented here show vast generalizations of these facts. Up to now, there is only one...