Differential Geometry | Topology Answers

Find the asymtotes of the curve xu(x^2-y^2) +x^2+y^2-a^2.show that the eight points of intersection of the curve with its asymtotes lie on a circle whose centre is at the origin

For what n TS^n=R^n?

if A = 5t2 + tj-t3k and B = sin t1-costj evaluate d/dt (AXB)

Q. Compute the normal curvature of the circle γ(t)=(cost, sint, 1) on the elliptic paraboloid
σ(u,v)=(u,v,u^2+v^2)

Q. Compute the first fundamental form and second fundamental form of the elliptical paraboloid σ(u,v)=(u, v,〖 u〗^2+v^2)

Q. Calculate the first fundamental forms of the following surfaces:
1) Sphere: σ(θ,φ) =(cosθcosφ, cosθsinφ,sinθ)
2) A generalized cylinder: σ(u,v) =γ(u)+Va

Define surface.

Q. The unit sphere S^2 defined by
σ(θ,φ) =(cosθcosφ,cosθsinφ,sinθ)
σ͂(θ,φ) =(-cosθcosφ,-sinθ,-cosθsinφ)

Q. Show that the circular cylinder S={(x,y,z)∈R^3 |x^2+y^2=1} can be covered by a single surface patch and so a surface.

Hello, I need help with one of my assignment questions. How do you calculate the diameter of a pipe needed to water a track with only knowing the flow rate of 0.7 l/sec