Given

  • Surface in 3D space (torus):
  • x = (a+b*cos(u))*cos(v)
  • y = (a+b*cos(u))*sin(v)
  • z = b*sin(v)
  • in rectangular coordinate system

Calculate

  • 1. Surface metric (first fundamental form)
  • 2. Second fundamental form
  • 3. Mean curvature vector
  • 4. Connection, Christoffel symbols, curvature
  • 5. Riemann and Ricci tensors
  • 6. Gauss curvature
  • 7. Laplace operator
  • Run atlas 2D/3D Wizard and press NEXT button
  • Choose  3D - space and press NEXT button
  • Select RECTANGULAR coordinate system and press NEXT button
  • Select SURFACE and press NEXT button
  • Enter the surface equations and press NEXT button (u, v are surface coordinates)
  • Press Check-Out button or just skip this step and press NEXT button
  • Specify a worksheet to save the Maple™ code (output.mws by default).
  • Press FINISH button and execute in Maple™ the generated file

Result of the execution

You will see the results of the execution in the worksheet: surface metric, second fundamental form, mean curvature vector, connection, Christoffel symbols, curvature, Riemann and Ricci tensors, Gauss curvature, Laplace operator.

It takes 2 minutes to solve this problem from the beginning to the end! Just try it.