Proceedings of the Centre for Mathematics and its Applications

Introduction to differential geometry

Robert Bartnik

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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

Source
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

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


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