Differential Approach to Geometry

Francis Borceux is Professor of mathematics at the University of Louvain since many years. He has developed research in algebra and essentially taught geometry, number theory and algebra courses and he has been dean of the Faculty of Sciences of his University and chairman of the Mathematical Committee of the Belgian National Scientific Research Foundation.

"The book has a very logical structure and is written in a lively fashion. Ultimately it will serve as a very useful material for undergraduate students learning differential geometry, but it is also recommended basically to all master or PhD students in physics and mathematics." (Arpad Kurusa, Acta Scientiarum Mathematicarum, Vol. 81 (3-4), 2015) "This is the third volume of the geometric trilogy which is an introductory three-volume book in geometry. ... The book contains interesting exercises which allow the reader to practice the techniques and notions treated in it as well as problems which have more theoretical interest and give the reader the possibility to explore deeper issues of geometry. ... it is written with love and care. It generates interest and enthusiasm to the reader and inspires for further study of geometry." (Charalampos Charitos, zbMATH, Vol. 1290, 2014)

• Introduction.- Preface.- 1.The Genesis of Differential Methods.- 2.Plane Curves.- 3.A Museum of Curves.- 4.Skew Curves.- 5.Local Theory of Surfaces.- 6.Towards Riemannian Geometry.- 7.Elements of Global Theory of Surfaces.- Appendices: A.Topology.- B.Differential Equations.- Index.- Bibliography. ​