Description
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
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
