Differential Geometry and Tensors

Contents: Preface. A. Differential Geometry: Vector notations. 1. Theory of curves in space. 2. Envelops and developable. 3. Curves on surfaces and fundamental magnitudes. 4. Curvature of surfaces and lines of curvature. 5. Fundamental equations of surface theory. 6. Geodesics. B. Tensors: 1. Introduction. 2. Tensor algebra. 3. Tensor calculus. 4. Christoffel symbols, covariant differentiation, and their properties. 5. Riemann symbols. 6. Geodesics, Reimannian coordinates, geodesic coordinates and parallelism of vectors. 7. Differentiable manifolds and Reimannian manifolds. Index.

From the Preface: "The aim of this book is to provide a textbook on Differential Geometry and Tensors, which is being taught in the present three years degree course in mathematics. The purpose of this book is to give a simple, lucid, rigorous and comprehensive account of fundamental notions of Differential Geometry and Tensors. The book is self contained and divided into two parts, section - A and section - B. Section - A deals with differential geometry and section - B devoted to the study of tensors. Numerous examples are either wanted out are given as an exercise in both the sections, to grasp the subject easily and clearly."