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.