Exotic Steiner chains in Miquelian Möbius planes of odd order
-
Norbert Hungerbühler
and
Gideon Villiger
Abstract
In the Euclidean plane, two circles that intersect or are tangent clearly do not carry a finite Steiner chain of circles. We show that such exotic Steiner chains exist in finite Miquelian Möbius planes of odd order. We obtain explicit conditions in terms of the order of the plane and the capacitance of the two carrier circles for the existence, length, and number of Steiner chains.
Acknowledgements
We would like to thank the referee for his or her careful reading and the valuable remarks which greatly helped to improve this article.
Communicated by: G. Korchmáros
References
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Articles in the same Issue
- Frontmatter
- Complex geodesics in convex domains and ℂ-convexity of semitube domains
- Triharmonic Riemannian submersions from 3-dimensional space forms
- Ricci almost solitons and contact geometry
- Shapes of centrally symmetric octahedra with prescribed cone-deficits
- Equivariant Ulrich bundles on exceptional homogeneous varieties
- Exotic Steiner chains in Miquelian Möbius planes of odd order
- Double cover K3 surfaces of Hirzebruch surfaces
- The dual cone of sums of non-negative circuit polynomials
- Einstein tori and crooked surfaces
- Compact null hypersurfaces in Lorentzian manifolds
- Hyperbolic torsion polynomials of pretzel knots
- Geodesic orbit Randers metrics on spheres
- Rational conic fibrations of sectional genus two
- Hodge numbers of hypersurfaces in ℙ4 with ordinary triple points
Articles in the same Issue
- Frontmatter
- Complex geodesics in convex domains and ℂ-convexity of semitube domains
- Triharmonic Riemannian submersions from 3-dimensional space forms
- Ricci almost solitons and contact geometry
- Shapes of centrally symmetric octahedra with prescribed cone-deficits
- Equivariant Ulrich bundles on exceptional homogeneous varieties
- Exotic Steiner chains in Miquelian Möbius planes of odd order
- Double cover K3 surfaces of Hirzebruch surfaces
- The dual cone of sums of non-negative circuit polynomials
- Einstein tori and crooked surfaces
- Compact null hypersurfaces in Lorentzian manifolds
- Hyperbolic torsion polynomials of pretzel knots
- Geodesic orbit Randers metrics on spheres
- Rational conic fibrations of sectional genus two
- Hodge numbers of hypersurfaces in ℙ4 with ordinary triple points
