ABSTRACT

An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential

chapter 1|7 pages

TOPOLOGY

chapter 2|22 pages

DIFFERENTIAL CALCULUS IN BANACH SPACES

chapter 3|7 pages

EXERCISES

chapter |3 pages

INTRODUCTION

chapter 1|10 pages

DIFFERENTIABLE MANIFOLDS

chapter 2|9 pages

DIFFERENTIABLE MAPPINGS

chapter 3|6 pages

SUBMANIFOLDS

chapter 4|6 pages

EXERCISES

chapter 1|9 pages

TANGENT VECTOR

chapter 2|3 pages

TANGENT SPACE

chapter 3|4 pages

DIFFERENTIAL AT A POINT

chapter 4|4 pages

EXERCISES

chapter |2 pages

INTRODUCTION

chapter 1|3 pages

TANGENT BUNDLE

chapter 2|1 pages

VECTOR FIELD ON MANIFOLD

chapter 3|5 pages

LIE ALGEBRA STRUCTURE

chapter 4|9 pages

ONE-PARAMETER GROUP OF DIFFEOMORPIDSMS

chapter 5|14 pages

EXERCISES

chapter 1|5 pages

COTANGENT BUNDLE AND COVECTOR FIELD

chapter 2|14 pages

TENSOR ALGEBRA

chapter 3|9 pages

EXERCISES

chapter 1|9 pages

EXTERIOR FORM AT A POINT

chapter 2|5 pages

DIFFERENTIAL FORMS ON A MANIFOLD

chapter 3|3 pages

PULL-BACK OF A DIFFERENTIAL FORM

chapter 4|4 pages

EXTERIOR DIFFERENTIATION

chapter 5|4 pages

ORIENTABLE MANIFOLDS

chapter 6|7 pages

EXERCISES

part |1 pages

LECTURE 6: LIE DERIVATIVE-LIE GROUP

chapter 1|13 pages

LIE DERIVATIVE

chapter 2|5 pages

INNER PRODUCT AND LIE DERIVATIVE

chapter 3|3 pages

FROBENIUS THEOREM

chapter 4|4 pages

EXTERIOR DIFFERENTIAL SYSTEMS

chapter 5|3 pages

INV ARIANCE OF TENSOR FIELDS

chapter 6|10 pages

LIE GROUP AND ALGEBRA

chapter 7|11 pages

EXERCISES

chapter 1|4 pages

n-FORM INTEGRATION ON n-MANIFOLD

chapter 2|1 pages

INTEGRAL OVER A CHAIN

chapter 3|3 pages

STOKES' THEOREM

chapter 4|5 pages

AN INTRODUCTION TO COHOMOLOGY THEORY

chapter 5|5 pages

INTEGRAL INVARIANTS

chapter 6|4 pages

EXERCISES

chapter 1|28 pages

RIEMANNIAN MANIFOLDS

chapter 2|15 pages

AFFINE CONNECTION

chapter 3|2 pages

GEODESIC AND EULER EQUATION

chapter 5|15 pages

EXERCISES

chapter 1|4 pages

CLASSICAL MECHANICS SPACES AND METRIC

chapter 6|12 pages

ISOLATING INTEGRALS

chapter 7|4 pages

EXERCISES

chapter |3 pages

PRELIMINARIES

chapter 1|16 pages

SYMPLECTIC GEOMETRY

chapter 2|11 pages

CANONICAL TRANSFORMATIONS IN MECHANICS

chapter 3|7 pages

HAMILTON-JACOBI EQUATION

chapter |14 pages

EXERCISES