Differential Geometry And Tensors by 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 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; and, 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; and, differentiable manifolds, charts, atlases.
Audience of the Book :
|This book has been systematically organized in a easy way to read. This book will surve as suitable text cum reference book for the students of M.Sc. and B.Sc. honours from various universities.|
The main features of the book are as follows:
1. Theory of curves, envelopes and developables.
2.Curves on surfaces and fundamental magnitudes, curvature of surfaces and lines of curvature.
3.Fundamental equations of surface theory.
Table of Contents:
1.Differential Geometry: Vector Notations
2.Theory of Curves in Space
3.Envelopes and Developables
4.Curves on Surfaces and Fundamental Magnitudes
5.Curvature of Surfaces and Lines of Curvature: Local Non-Intrinsic Properties of Surface
6.Fundamental Equations of Surface Theory
4.Christoffel Symbols, Covariant Differentiation, and their Properties
6.Geodesics, Riemannian Coordinates, Geodesic Coordinates and Parallelism of Vectors
7.Differentiable Manifolds and Riemannian Manifolds