An Introduction to Smooth Manifolds

Targeted to graduate students of mathematics, this book discusses major topics like the Lie group in the study of smooth manifolds. It is said that mathematics can be learned by solving problems and not only by just reading it. To serve this purpose, this book contains a sufficient number of examples and exercises after each section in every chapter. Some of the exercises are routine ones for the general understanding of topics. The book also contains hints to difficult exercises. Answers to all exercises are given at the end of each section. It also provides proofs of all theorems in a lucid manner. The only pre-requisites are good working knowledge of point-set topology and linear algebra.

Discusses topics on differential forms, Lie group and action of a Lie group on a smooth manifold Includes topics in calculus on Rn, manifold theory and one-parameter group of transformations Presents the subject matter lucidly, in an orderly and systematic manner

Auteur
MANJUSHA MAJUMDAR (TARAFDAR), PhD, former Professor of Pure Mathematics at the University of Calcutta, India. Her main interest lies in smooth manifolds. She has published a number of research papers in several international journals of repute. Under her supervision, 10 students have already been awarded their PhD degrees. She is member of many national and international mathematical societies and serves on the editorial board of several journals of repute. She has visited several institutions in India and abroad on invitation. She is the Principal Investigator of the prestigious e-PG Pathshala in Mathematics and MOOC in Mathematics, recommended by the Ministry of Human Resource Development, the Government of India. She co-authored a book entitled, Differential Geometry. ARINDAM BHATTACHARYYA, PhD, is Professor, Department of Mathematics, Jadavpur University, Kolkata, India. His main interest lies in smooth manifolds, geometric flows and computational geometry. He has published a number of research papers in several international journals of repute. Under his supervision, 19 research scholars have already been awarded their PhD degrees and 8 are pursuing their research. He is member of many national and international mathematical societies and serves on the editorial board of several journals of repute. He has visited several institutions in India and abroad on invitation. He has organized several international conferences and research schools in collaboration with internationally reputed mathematical organizations. He is the Course Coordinator of Differential Geometry of the prestigious e-PG Pathshala in Mathematics and MOOC in Mathematics, recommended by the Ministry of Human Resource Development, the Government of India and of Netaji Subhas Open University, India. He co-authored a book entitled, Differential Geometry with Prof. Manjusha Majumdar.

Contenu

1. Calculus on Rn.- 2. Manifold Theory.- 3. Differential Forms.- 4. Lie Group.