Differential Geometry and Tensors

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 in two parts. Section A deals with Differential Geometry and Section B is devoted to the study of Tensors. Section A deals with: Theory of curves, envelopes and developables. Curves on surfaces and fundamental magnitudes, curvature of surfaces and lines of curvature. Fundamental equations of surface theory. Geodesics. Section B deals with: Tensor algebra. Tensor calculus. Christoffel symbols and their properties. Riemann symbols and Einstein space, and their properties. Physical components of contravariant and covariant vectors. Geodesics and Parallelism of vectors. Differentiable manifolds, charts, atlases.