The 2-manifold M in R4 given by the equations 2x1 + x4 = 0, x2 - ...

[Lisaclaire]

The 2-manifold M in R⁴ given by the equations 2x₁ + x₄ = 0, x₂ - 5x₃ = 0, 0 < x₂ < 1, 0 < x₄ < 1 has normals n₁ = 2e₁+ e₄, n₂ = e₂ - 5 e₃. It is oriented by the 2-form ω(x)(v₁, v₂) = det(n₁ n₂ v₁ v₂). Let be a parametrization for M. Which of the following statements is true?
◦ P is orientation reversing for M, but no orientation preserving parametrization for M exists.
◦ P is orientation preserving for M.
◦ P does not determine an orientation for M.
◦ P is orientation reversing for M, but q(u) = (u₁, 5u₂, u₂, -2u₁) would be orientation preserving parametrization for M.
◦ P is orientation reversing for M, but q(u) = (-u₁, 5u₂, u₂, 2u₁) would be an orientation-preserving parametrization for M.

[reversalruiz]

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[Lisaclaire]

Thanks for the timely response, appreciate it

[Liamb2179]

Gracias!