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Differential Geometry and Tensors

K.K. Dube

ISBN: 9789389520620

384 pages

INR 425

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: 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