Calculating Gaussian Curvature Using Differential Forms - Maple Application Center
Application Center Applications Calculating Gaussian Curvature Using Differential Forms

Calculating Gaussian Curvature Using Differential Forms

Author
: Dr. Frank Wang
Engineering software solutions from Maplesoft
This Application runs in Maple. Don't have Maple? No problem!
 Try Maple free for 15 days!

Riemannian geometry is customarily developed by tensor methods, which is not necessarily the most computationally efficient approach.  Using the language of differential forms, Elie Cartan's formulation of the Riemannian geometry can be elegantly summarized in two structural equations.  Essentially, the local curvature of the manifold is a measure of how the connection varies from point to point.  This Maple worksheet uses the DifferentialGeometry package to solves three problems in Harley Flanders' book on differential forms to demonstrate the implementation of Cartan's method.  

Application Details

Publish Date: December 09, 2014
Created In: Maple 18
Language: English

More Like This

Matrix Representation of Quantum Entangled States: Understanding Bell's Inequality and Teleportation
Application of the Lambert W Function to the SIR Epidemic Model
1
Rosalind Franklin's X-ray diffraction Photograph of DNA
Visualizing the Laplace-Runge-Lenz Vector
Richard Dawkins' Battle of the Sexes Model
Numerical Solution of a Mechanics Braintwister Problem
1
Alexander Friedmann's Cosmic Scenarios
Demonstrating Soliton Interactions using 'pdsolve'
1
Standard Map on a Torus
El Niño Temperature Anomalies Modeled by a Delay Differential Equation
Propagation of Plane Gravitational Waves
The Hawk-Dove-Retaliator Game