An Introduction to Differential Geometry with Maple (Lecture given at Park City Mathematics Institute, July 5, 2013)

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The Differential Geometry software project provides a comprehensive suite of programs for computations in differential geometry and Lie theory with applications to the calculus of variations, general relativity and geometric methods in differential equations. In this talk I will survey the general objectives and design goals of this software project, review current and future developments and give a couple of brief demonstrations. In the first demonstration I will study the remarkable properties of the Eguchi-Hanson gravitational instanton. In the second demonstration I will construct some homogeneous Einstein metrics, and in third example I will illustrate some commands which support the analysis of simple Lie algebras.

The DifferentialGeometry software is part of the Maple distributed library and is already installed on your computer if you have any version of Maple, release 11 or higher.

Overview.pdf (106 kB)

Demo1-GettingStarted.pdf (201 kB)
Getting Started

Demo2-ExactSolutionsinGR.pdf (221 kB)
Solutions of the Einstein Equations

Demo3-Octonions.pdf (247 kB)
The Octonians and the Exceptional Group G2

Demo4-EguchiHansonMetric.pdf (264 kB)
The Eguchi-Hanson Metric

Demo5-HomogeneousEinsteinMetrics.pdf (275 kB)
Homogeneous Einstein Spaces

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