DIFFERENTIAL GEOMETRY
AN INTEGRATED APPROACH

This book is a unique combination of the classical and modern differential geometric techniques. It covers the differential geometry of curves and surfaces, discusses forms and tensors as geometric objects, presents the elementary theory of Lie groups, covering spaces and Jacobi fields, etc., and proves results like Gauss-Bonnet theorem and Hopf-Rinow theorem.

In its approach and style, it is designed to the specific needs of students. Included are appropriate solved examples and problems with answers which link the fundamental theory with computational techniques. Hints of comparatively difficult problems are given. Proofs of lemmas and theorems, presented with clarity, are often followed by explanatory notes. With its emphasis on integration, its student orientation and comprehensive coverage, the book should prove a useful undergraduate and postgraduate text.