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Differential Geometry and Tensors

Author : K K Dube

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: 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

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.

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