Integrable wire billiards in R^3

Construct integrable examples of wire billiards in three dimensions defined by closed non-planar curves, or prove that none exist.

Background

Wire billiards reflect along a curve so that incident and outgoing chords form equal angles with the tangent, leading to multi-valued dynamics in general; explicit integrable examples are known in higher dimensions.

The authors note integrable closed wire examples exist in Rⁿ for n>3 and ask whether any exist in R^3.

References

In this section we formulate natural open questions related to the results discussed in previous sections. (1) Are there integrable examples of wire billiards in $\mathbb R^3$? In , integrable examples of closed wires are found in $\mathbb R^{n}, n>3$?

— Integrable Billiards and Related Topics (2510.03790 - Bialy et al., 4 Oct 2025) in Section 9 (Open questions), Subsection Wire and cone billiards, item (1)

Integrable wire billiards in R^3

Background

References

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