Let s be the ruled surface generated by the binormals

Assignment Help Mathematics

Reference no: EM13714127

1. Let σ be the ruled surface generated by the binormals b of a unit-speed curve γ:

σ(u, v) = γ(u) + vb(u).

Show that the first fundamental form of σ is

(1 + v2τ 2) du2 + dv2,

where τ is the torsion of γ.

2. Let f be a smooth function and let

σ(u, v) = (u cos v, u sin v, f(u))

be the surface obtained by rotating the curve z = f(x) in the xz-plane around

the z-axis.

(i) Find all functions f for which σ is conformal.

(ii) Find all functions f for which the surface patch σ.

Reference no: EM13714127

Questions Cloud

Long-parkers and short-parkers arrive at a parking : Long-parkers and short-parkers arrive at a parking place for cars according to independent Poisson processes with respective rates of λL = 4 and λS = 6 cars per hour. The parking place has room for only 2 cars. Each arriving car which finds bot..

Brooke has to set up 70 chairs in equal rows : Brooke has to set up 70 chairs in equal rows for the class talent show. But,there is not room for more than 20 rows. What are the possible number of rows that Brooke could use?

Determining the number of solutions of a system : Determining the number of solutions of a system by finding the slope and the y intercept of a graph of each line in the system of equations?

Condition the pressure p and volume v of gas satisfy : Under a certain condition the Pressure p and volume v of gas satisfy the equation p^5v^7 =1000. Suppose that at some moment the volume of the gas is 4liters; the pressure is 200units, and the pressure at the rate 5units per second. Find the ra..

Let s be the ruled surface generated by the binormals : 1. Let σ be the ruled surface generated by the binormals b of a unit-speed curve γ: σ(u, v) = γ(u) + vb(u). Show that the first fundamental form of σ is

Describe the transitive subgroups of sn for n = 3, 4, 5 : 1. Describe the transitive subgroups of Sn for n = 3, 4, 5 2. Find the invariant factors of Z/4Z ⊕ Z/9Z ⊕ Z/50Z. P.S : Please prove the question with step by step.

The heat pumps coefficient of performance : The interior of a building is maintained at 23oC by a heat pump cycle operating at steady state while receiving thermal energy from well water at 12oC. The thermal energy discharged to the building is at a rate of 116, 250 kJ/h.

Find the optimal solution for all values : Deterministic models / linear programming. Please help asap 1. Consider the following parametric problem: z(θ) = min - 10x1 + 16x2 - x3 x1 - 2x2 + x3 ≤ 2 + 2θ x1 - x2 ≤ 4 + θ x1, x2, x3 ≥ 0,

Refrigeration cycle operating between cold-hot reservoirs : A refrigeration cycle maintains a clean room at 68oF by removing energy entering the room by heat transfer at the rate of 0.21 Btu/s. The cycle rejects energy by heat transfer to the outdoors where the temperature is 80oF.

User Account

All Pages