## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- Instructional Workshop on Analysis and Geometry, Part 2. Tim Cranny and John Hutchinson, eds. Proceedings of the Centre for Mathematics and its Applications, v. 34. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1996), 125 - 163

### Introduction to differential geometry

#### Abstract

These notes are designed to give a heuristic guide to many of the basic constructions of differential geometry. They are by no means complete; nor are they at all exhaustive. Some of the elementary topics which would be covered by a more complete guide are: geodesics and conjugate points; Lie derivative and the flow of a vector field; coordinate construction techniques; GauB-Bonnet Theorem; Bochner formulae; de Rham cohomology; Lie groups. Despite these and other omissions, I hope that the notes prove useful in motivating the basic geometric constructions on a manifold.

#### Article information

**Dates**

First available in Project Euclid:
18 November 2014

**Permanent link to this document**

https://projecteuclid.org/
euclid.pcma/1416323491

**Mathematical Reviews number (MathSciNet)**

MR1394689

**Zentralblatt MATH identifier**

0884.53001

#### Citation

Bartnik, Robert. Introduction to differential geometry. Instructional Workshop on Analysis and Geometry, Part 2, 125--163, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1996. https://projecteuclid.org/euclid.pcma/1416323491