The concept of a differentiable manifold is introduced in a simple manner without going into its topological structure. Subsequently the reader is led to the same conceptual details as are found in other texts on the subjects. Since calculus on a differentiable manifold is done via the calculus on Rn, a preliminary chapter on the calculus on Rn is added. While introducing concepts such as tangent and cotangent bundles, tensor algebra and calculus, Riemannian geometry etc., enough care is taken to provide many details which enable the reader to grasp them easily. The material of the book has been tried in class-room successfully. Queries raised by the students have helped us to improve the presentation.
Krishna S. Amur.: Department of Mathematics, Karnataka University Dharwad D. J. Shetty.: Padmavathi College, #7 Chinde Blocks Behind K.E.B. Office, Gulbarga C. S. Bagewadi.: Department of Mathematics, Kuvempu University Shankaraghatta
Preface / Differential Calculus on Rn and Related Topics / Differentiable Manifolds / Tangent, Cotangent Spaces and Bundles / One Parameter Group and Lie Derivatives / Tensor Algebra and Calculus / Connections / Riemannian Manifolds / Submanifolds / Bibliography / Index.