# The projection of the curvature vector onto tangent plane on Cone

Draw diagrams for cone ( with cone angle less than $360^{\circ}$) to show that the geodesics (generating ray and the warp around) have a projection of the curvature vector onto the tangent plane that is $0$. Also, consider a circle on the cone and show that it has a non-zero projection onto the tangent plane.

I am wondering if someone would be able to help me out with this question. I do know how they look on Cylinder and sphere but I do not how they look on cone. How would I draw a cone angle less than $360^{\circ}$.

• Just draw any old right circular cone. You can construct one out of paper by drawing a pacman shape (remove a sector from a filled-in circle) and taping the straight edges together. – Ted Shifrin Jul 20 '16 at 18:33
• Seconding Ted's suggestion to build a model, which takes less than one minute: Slit an ordinary sheet of paper from an edge to near the middle, then pull the cut edges "toward" each other so the paper overlaps itself. The interior end of the slit becomes the cone's vertex. Any straight line drawn on the paper (and not crossing the slit) becomes a geodesic on the cone. – Andrew D. Hwang Jul 21 '16 at 12:29
• Thank you ! how would I create a wrap around cone. Where the tangent plane would be laying. – ADAM Jul 21 '16 at 13:37