In this matlab program, you can calculate the following:
- metric tensor
- riemannian connection
- riemann curvature tensor
- ricci curvature tensor
- scalar curvature
- gauss Curvature
- parallel transport
- geodesic
- visualization of surface
- visualization of parallel transport
- visualization of scalar curvature
- visualization of geodesic
It is recommended to use the latest version of matlab
Input: parametric equation
This routine will automatically calculate metrics induced by the ambient three-dimensional euclidean space.
sphere geodesic |
sphere parallel |
torus parallel |
torus geodesic |
torus curvature |
hyperbolic parallel |
hyperbolic geodesic |