can one construct a solid Klein bottle - a 3 manifold whose boundary is a Klein bottle as follows.(adsbygoogle = window.adsbygoogle || []).push({});

- Start with a solid cylinder and identify the two bounding disks by a reflection.

- The boundary becomes a Klein bottle but is this a smooth manifold whose boundary is this Klein bottle?

- If so does this manifold deform onto its central circle just as a solid torus would?

- Since reflection is an isometry of the disk, can one give this manifold a flat metric?

In general if the boundaries of two Riemannian manifolds are identified by an isometry do their metrics extend?

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# A solid Klein bottle?

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