A Primer On Smooth Manifolds

A Primer On Smooth Manifolds
by: Luca Vitagliano (Author)
Publisher:World Scientific Publishing Co Pte Ltd
Publication Date: 27 Mar. 2024
Language:English
Print Length:300 pages
ISBN-10:981128394X
ISBN-13:9789811283949
Book Description
Differential Geometry is one of the major branches of current Mathematics, and it is an unavoidable language in modern Physics. The main characters in Differential Geometry are smooth manifolds: a class of geometric objects that locally behave like the standard Euclidean space.The book provides a first introduction to smooth manifolds, aimed at undergraduate students in Mathematics and Physics. The only prerequisites are the Linear Algebra and Calculus typically covered in the first two years. The presentation is as simple as possible, but it does not sacrifice the rigor.The lecture notes are divided into 10 chapters, with gradually increasing difficulty. The first chapters cover basic material, while the last ones present more sophisticated topics. The definitions, propositions, and proofs are complemented by examples and exercises. The exercises, which include part of the proofs, are designed to help the reader learn the language of Differential Geometry and develop their problem-solving skills in the area. The exercises are also aimed at promoting an active learning process. Finally, the book contains pictures which are useful aids for the visualization of abstract geometric situations. The lecture notes can be used by instructors as teaching material in a one-semester course on smooth manifolds.
About the Author
About the Author Luca Vitagliano is a Full Professor of Geometry at the University of Salerno, Italy, where he regularly teaches Geometry courses to bachelor, master and PhD students. His main research interests lie in Differential Geometry, with a slight emphasis on those aspects that are inspired by Mathematical Physics. He is (co)author of around 40 scientific papers in the field, published in distinguished international mathematical journals and has been invited to present his results at several international conferences. He is an editor of the following journals: International Journal of Geometric Methods of Modern Physics (Worlds Scientific), Differential Geometry and its Applications (Elsevier), and Journal of Nonlinear Mathematical Physics (Springer).