A Textbook of Differential Geometry  (Paperback, M. L. Jain, Anu Sharma, Kanika Goyal)

The present book is designed to meet the requirements of students persuing U.G. and P.G. courses of various Indian universities as well as for students preparing for various competitive and entrance examinations. In this book an humble attempt has been made to present the subject matter in a comprehensive, lucid and easy to understand style. At the same time the matter is rigorous and exhaustive and nothing of importance has been omitted. The special feature of the book are the notes and remarks given wherever it is felt that the students need an explanation of any particular point. Keeping in the mind that this subject is generally considered tough by the student fraternity, quite a number of illustrative examples are given at the end of each topic. In fact, almost all types of questions have been tackled in these solved examples. The questions given in the unsolved exercises are based of these solved examples so that the students can attempt these questions on their own. The articles and results, which constitute a fair amount of the subject matter, have been discussed in a very simple and easy language. Contents 1. Curves in Space 2. Circle of Curvature and Spherical Curvature 3. Helices and Spherical Indicatrices 4. Involutes and Evolutes 5. Concept of a Surface, Envelopes and Developable 6. Fundamental Forms of Surfaces 7. Local Non-Intrinsic Properties of a Surface 8. Conjugate and Asymptotic Lines, Fundamental Equations of Surface Theory 9. Geodesics