If a non-orientable manifold (like a Möbius strip) is embedded in 3D space and continuously deformed, which consequence relating to vector fields is most likely?

💡 Explanation

Because a non-orientable manifold lacks a consistent normal vector field, any attempt to define a smooth, non-vanishing vector field across the entire surface results in singularities due to the Hairy Ball Theorem. Therefore, singularities must occur, rather than parallel transport being preserved, because non-orientability prevents consistent directionality.

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