Synopsis "Projective Differential Geometry of Curves and Surfaces (in English)"
Projective Differential Geometry of Curves and Surfaces is a comprehensive textbook written by Ernest Preston Lane, an American mathematician. The book explores the principles and applications of projective geometry, a branch of mathematics that deals with the properties of geometric figures that remain invariant under projection. The author focuses on the study of curves and surfaces in projective space, and provides a detailed analysis of their differential geometry. The book is divided into two parts. The first part covers the fundamentals of projective geometry, including projective transformations, duality, and the cross-ratio. The author then introduces the concept of differential geometry, including the study of curves and surfaces in Euclidean space. The second part of the book delves deeper into the study of curves and surfaces in projective space. The author discusses the theory of curves, including the classification of planar curves, and the geometry of surfaces, including the classification of quadric surfaces. The book is written in a clear and concise manner, making it accessible to both students and researchers in mathematics. It includes numerous examples and exercises to help readers develop a deeper understanding of the material. This book is an essential resource for anyone interested in the study of projective geometry and its applications to differential geometry.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.
