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.

some sample outputs

sphere geodesic

sphere parallel

torus parallel

torus geodesic

torus curvature

hyperbolic parallel

hyperbolic geodesic