Central figure-8 cross-cuts make surfaces cylindrical
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Bruce Solomon
Abstract
Let M be a complete connected C2-surface in ℝ3 in general position, intersecting some plane along a clean figure-8 (a loop with total curvature zero) and such that all compact intersections with planes have central symmetry. We prove that M is a (geometric) cylinder over some central figure-8. On the way, we establish interesting facts about centrally symmetric loops in the plane; for instance, a clean loop with even rotation number 2k can never be central unless it passes through its center exactly twice and k = 0.
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© 2017 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Ricci solitons on four-dimensional Lorentzian Walker manifolds
- The exterior splash in PG(6, q): carrier conics
- Central figure-8 cross-cuts make surfaces cylindrical
- Vieta’s formulae for regular polynomials of a quaternionic variable
- On characterizations of sausages via inequalities and roots of Steiner polynomials
- On maximal symplectic partial spreads
- Helly numbers of algebraic subsets of ℝd and an extension of Doignon’s Theorem
- A maximum problem of S.-T. Yau for variational p-capacity
- Drapeable unit arcs fit in the unit 30° sector
- Uniform Lie algebras and uniformly colored graphs
- A Krasnosel’skii-type theorem for an enlarged class of orthogonal polytopes
Articles in the same Issue
- Frontmatter
- Ricci solitons on four-dimensional Lorentzian Walker manifolds
- The exterior splash in PG(6, q): carrier conics
- Central figure-8 cross-cuts make surfaces cylindrical
- Vieta’s formulae for regular polynomials of a quaternionic variable
- On characterizations of sausages via inequalities and roots of Steiner polynomials
- On maximal symplectic partial spreads
- Helly numbers of algebraic subsets of ℝd and an extension of Doignon’s Theorem
- A maximum problem of S.-T. Yau for variational p-capacity
- Drapeable unit arcs fit in the unit 30° sector
- Uniform Lie algebras and uniformly colored graphs
- A Krasnosel’skii-type theorem for an enlarged class of orthogonal polytopes
