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.

Contents: Section A: Differential Geometry: Vector Notations / Theory of Curves in Space / Envelopes and Developables / Curves on Surfaces and Fundamental Magnitudes / Curvature of Surfaces and Lines of Curvature: Local Non-Intrinsic Properties of Surface / Fundamental Equations of Surface Theory / Geodesics / Section B: Tensor: Introduction / Tensor Algebra / Tensor Calculus / Christoffel Symbols, Covariant Differentiation, and their Properties / Riemann Symbols / Geodesics, Riemannian Coordinates, Geodesic Coordinates and Parallelism of Vectors / Differentiable Manifolds and Riemannian Manifolds / Index